# Schedule

*Main Foyer*

*Room 200*

About the importance of discrete product and chain rules for stable high order methods

*Room 200*

**Chair:** Mark H. Carpenter (NASA Langley Research Center)

Download to calendar

#### Abstract

On paper, high order methods offer great capabilities. The general idea everyone agrees with is that for small grid resolution parameter, h, a high order method will always outrun low order variants due to the favorable asympotic behaviour of the discretisation errors. However, the luxury of having simulations with small h (i.e. well resolved approximations) is something that typically only academia can afford.

For marginally resolved simulations of non-linear PDEs, such as the compressible Navier-Stokes (NS) equations or the magnetohydrodynamics (MHD) equations, we observe that high order methods are prone to aliasing instabilities, which can lead to total failure and breakdown of the algorithms. Aliasing issues are provoked by insufficient discrete integration precision, collocation of non-linear terms, polynomial ansatz spaces for rational functions, and, again, by insufficient grid resolution.

The aim of this talk is to discuss a remedy for aliasing issues and present its connection to discrete product and chain rules. By using building blocks from summation-by-parts finite difference, first order finite volume and Gauss-Lobatto-Legendre spectral element methods, we show how to construct nodal high order discontinuous Galerkin methods that are discretely kinetic energy preserving and/or entropy stable on unstructured hexahedral curvilinear grids in three spatial dimensions for the compressible NS equations, the resistive MHD equations, and similar nonlinear systems.

*Room 200*

**Organisers:**Giancarlo Sangalli (Università degli Studi di Pavia), Lorenzo Tamellini (IMATI-CNR)

*Weighted quadrature for isogeometric analysis*

**Presenter:**Giancarlo Sangalli, Università degli Studi di Pavia

*Efficient Quadrature for High Order Isogeometric Method*

**Presenter:**Francesco Calabrò, U. Cassino

*A matrix-free implementation for $k$-refined isogeometric analysis*

**Presenter:**Mattia Tani, University of Pavia

*Room 300*

**Presenter:**Arbaz Khan, University of Manchester, Manchester

*Scheme for evolutionary Navier-Stokes-Fourier system with temperature dependent material properties based on spectral/hp elements*

**Presenter:**Jan Pech, Institute of Thermomechanics of the Czech Academy of Sciences

*High performance numerical methods for the simulation of fluid surfaces*

**Presenter:**Daniel Santos-Oliván, Universitat Politècnica de Catalunya

*Conservative fourth-order finite-volume discretization of the Vlasov-Maxwell system in Cartesian and cylindrical axisymmetric geometries*

**Presenter:**G. V. Vogman, Lawrence Livermore National Laboratory

*Method of moving frames to solve time-dependent Maxwell’s equations on anisotropic curved surfaces*

**Presenter:**Sehun Chun, Yonsei University

*Room 640*

**Organisers:**Simona Perotto (Politecnico di Milano), Annalisa Quaini (University of Houston), Gianluigi Rozza (Scuola Internazionale Superiore di Studi Avanzati)

*A Spectral-Element Reduced Basis Method for Incompressible Flow Problems*

**Presenter:**Martin W. Hess, SISSA

*Reduced order modelling in bifurcating parametrised Von Kármán plate equations*

**Presenter:**Federico Pichi, SISSA, International School for Advanced Studies

*Coupling High-Order Methods to Reduced Order Models for the Accurate Solution of Elliptic Problems in Parameterized Geometries*

**Presenter:**Matteo Giacomini, Universitat Politècnica de Catalunya

**Presenter:**Haysam Telib, Optimad engineering

*Room 650*

**Organisers:**Ben Adcock (Simon Fraser University), Akil Narayan (University of Utah)

*Multilevel compressive sensing for high-dimensional parametric operator equations*

**Presenter:**Holger Rauhut, RWTH Aachen University

**Presenter:**Clayton Webster, University of Tennesee, Oak Ridge National Laboratory

*A connection between deep networks and sparse grids*

**Presenter:**Hadrien Montanelli, Columbia University

*Room 651*

**Organisers:**Sheehan Olver (Imperial College)

*Fast Direct Solvers with Spectrally-Driven Automatic Adaptive Refinement*

**Presenter:**Mike ONeil, Courant Institute, New York University

*Efficient direct solvers for a high-order accurate discretization scheme*

**Presenter:**Per-Gunnar Martinsson, University of Oxford

*A High Order Discretization Technique for Variable Coefficient Stokes' Equation*

**Presenter:**Adrianna Gillman, Rice University

*Fast direct least squares surface scattering without singular quadratures*

**Presenter:**Alex Barnett, Flatiron Institute

*Room 664*

**Organisers:**Iain Smears (University College London), Alexandre Ern (Ecole Nationale des Ponts et Chaussees, Inria Paris), Martin Vohralik (Inria Paris, Ecole Nationale des Ponts et Chaussees)

*Discrete $p$-Robust $H(\mathrm{div})$-Liftings and A Posteriori Estimates for Elliptic Problems with $H^{-1}$ Source Terms*

**Presenter:**Iain Smears, University College London

*Oscillation in a posteriori error estimation*

**Presenter:**Christian Kreuzer, TU Dortmund

*An Equilibration Based A Posteriori Error Estimate for the Biharmonic Equation*

**Presenter:**Joachim Schoeberl, TU Wien

*Near-Optimal Adaptive Approximation*

**Presenter:**Peter Binev, University of South Carolina

*Room 750*

**Organisers:**Bruno Després (University Paris 6 (UPMC, Sorbonne University)), Lise-Marie Imbert-Gérard (University of Maryland), Peter Monk (University of Delaware), Hélène Barucq (Inria/France), Anouk Nicolopoulos (University Paris 6 (UPMC, Sorbonne University)), Martin Campos-Pinto (CNRS (LJLL-UPMC, Sorbonne University)), Guillaume Morel (CEA/UPMC), Ahmed Ratnani (Max-Planck IPP)

*Trefftz discontinuous Galerkin method for Friedrichs systems with linear relaxation: application to the $P_N$ model*

**Presenter:**Guillaume Morel, CEA, DAM, DIF, F-91297 Arpajon, France; Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris, France

*High order approximations and the maximum principle*

**Presenter:**bruno despres, Sorbonne Université

*Higher Order Plane Wave Discontinuous Galerkin Methods*

**Presenter:**Peter Monk, University of Delaware

*Towards robust linear solvers for Computational Plasma Physics using Isogeometric Analysis*

**Presenter:**Ahmed Ratnani, Max-Planck IPP

*Room 751*

**Organisers:**Jae-Hun Jung (SUNY Buffalo, Ajou University), Wai-Sun Don (School of Mathematical Sciences, Ocean University of China)

*Progress in Accuracy & Stability Improvement of Nonlinear Filter Methods for Long Time Integration of Compressible Flows*

**Presenter:**H.C. Yee, NASA Ames Research Center

*High-Order Implicit Time-Stepping with High-Order Central ENO Methods for Unsteady Three-Dimensional Computational Fluid Dynamics Simulations*

**Presenter:**Thien Binh Nguyen, Monash University

*Recent developments in meshfree methods*

**Presenter:**Leevan Ling, Hong Kong Baptist University

*Jacobian-free Newton Krylov method for solving nonlinear PDEs*

**Presenter:**Misun Min, Argonne National Laboratory

*Main Foyer*

The Isogeometric Approach to Analysis

*Room 200*

**Chair:** Spencer Sherwin (Imperial College London)

Download to calendar

#### Abstract

The vision of Isogeometric Analysis was first presented in a paper published October 1, 2005 [1]. Since then it has become a focus of research within both the fields of Finite Element Analysis (FEA) and Computer Aided Design (CAD) and is rapidly becoming a mainstream analysis methodology and a new paradigm for geometric design [2]. The key concept utilized in the technical approach is the development of a new foundation for FEA, based on rich geometric descriptions originating in CAD, resulting in a single geometric model that serves as a basis for both design and analysis.

In this overview, I will describe some areas in which progress has been made in developing improved methodologies to efficiently solve problems that have been at the very least difficult, if not impossible, within traditional FEA. I will also describe current areas of intense activity and areas where problems remain open, representing both challenges and opportunities for future research (see, e.g., [3,4]).

References

[1] T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement, Computer Methods in Applied Mechanics and Engineering, 194, (2005) 4135-4195.

[2] J.A. Cottrell, T.J.R. Hughes and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester, U.K., 2009.

[3] Special Issue on Isogeometric Analysis, (eds. T.J.R. Hughes, J.T. Oden and M. Papadrakakis), Computer Methods in Applied Mechanics and Engineering, 284, (1 February 2015), 1-1182.

[4] Special Issue on Isogeometric Analysis: Progress and Challenges, (eds. T.J.R. Hughes, J.T. Oden and M. Papadrakakis), Computer Methods in Applied Mechanics and Engineering, 316, (1 April 2017), 1-1270.

*Room 200*

**Organisers:**Giancarlo Sangalli (Università degli Studi di Pavia), Lorenzo Tamellini (IMATI-CNR)

*Fast Multigrid Solvers for Isogeometric Discretizations of Curl-Div Problems*

**Presenter:**Hendrik Speleers, University of Rome "Tor Vergata"

*Multigrid methods for continuous and discontinuous Galerkin multipatch discretizations in Isogeometric Analysis*

**Presenter:**Stefan Takacs, Austrian Academy of Sciences

*High-order isogeometric spectral approximation properties*

**Presenter:**Quanling Deng, Curtin Universtiy

*Combining Isogeometric solvers and sparse grids technology*

**Presenter:**Lorenzo Tamellini, Consiglio Nazionale delle Ricerche

*Room 300*

**Organisers:**Oscar P. Bruno (Caltech, Pasadena CA), Catalin Turc (New Jersey Institute of Technology)

*Runge-Kutta Convolution Coercivity and Fast, Memory Efficient Computation*

**Presenter:**Lehel Banjai, Heriot-Watt University

*Optimized Schwartz methods for quasi-periodic scattering by layered media via robust boundary-integral equations*

**Presenter:**Catalin Turc, NJIT

**Presenter:**Timo Betcke, University College London

*Space-Time Discretization Methods for Wave Problems*

**Presenter:**Olaf Steinbach, TU Graz

*Room 309*

**Organisers:**Xiong Meng (Harbin Institute of Technology), Jennifer K. Ryan (University of East Anglia), Qiang Zhang (Nanjing University)

*Discontinuous Galerkin Methods with Staggered Hybridization for Linear Elastodynamics*

**Presenter:**Jie Du, Tsinghua University

*Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations*

**Presenter:**Eric Chung, CUHK

*Superconvergent HDG Methods for Third-Order Equations in One-Space Dimension*

**Presenter:**Bo Dong, University of Massachusetts Dartmouth

*Fourier type super convergence study on DDGIC and symmetric DDG Methods*

**Presenter:**Jue Yan, Iowa State University

*Room 640*

**Organisers:**Simona Perotto (Politecnico di Milano), Annalisa Quaini (University of Houston), Gianluigi Rozza (Scuola Internazionale Superiore di Studi Avanzati)

*High-Order Mesh Generation Based on Affine Combinations of Nodal Positions*

**Presenter:**Suzanne M. Shontz, University of Kansas

*Spatial eigensolution analysis of discontinuous spectral element methods: insights into under-resolved (turbulence) simulations*

**Presenter:**Rodrigo C. Moura, Technological Institute of Aeronautics

*Erosive Wear Evaluation Using Nektar++*

**Presenter:**Rodrigo Moura, Technological Institute of Aeronautics

*Room 650*

**Organisers:**Ben Adcock (Simon Fraser University), Akil Narayan (University of Utah)

*Polynomial approximation of high-dimensional functions on irregular domains*

**Presenter:**Ben Adcock, Simon Fraser University

*Correcting for unknown errors in sparse high-dimensional function approximation*

**Presenter:**Simone Brugiapaglia, Simon Fraser University, Pacific Institute for the Mathematical Sciences

*Assimilating data to optimally compute quantities of interest*

**Presenter:**Simon Foucart, Texas A&M University

*Neural Network Approximations in UQ*

**Presenter:**Christoph Schwab, ETH Zurich

*Room 651*

**Organisers:**Sheehan Olver (Imperial College)

*A low rank and spectrally-accurate elliptic PDE solver*

**Presenter:**Heather Wilber, Cornell University

*A fast algorithm for computing nonoscillatory phase functions*

**Presenter:**James Bremer, University of California, Davis

*Sparse spectral methods for PDEs on triangles with multivariate orthogonal polynomials*

**Presenter:**Sheehan Olver, Imperial College

*A spectral method for nonlocal diffusion operators on the sphere*

**Presenter:**Richard Mikael Slevinsky, University of Manitoba

*Room 664*

**Organisers:**Iain Smears (University College London), Alexandre Ern (Ecole Nationale des Ponts et Chaussees, Inria Paris), Martin Vohralik (Inria Paris, Ecole Nationale des Ponts et Chaussees)

*hp-Adaptive Newton-Discontinuous-Galerkin Finite Element Methods for Semilinear Elliptic Boundary Value Problems*

**Presenter:**Paul Houston, University of Nottingham

*An optimal adaptive Fictitious Domain Method*

**Presenter:**Rob Stevenson, University of Amsterdam

*hp-AFEM for Eigenvalue Approximations*

**Presenter:**Claudio Canuto, Politecnico di Torino, Turin Italy

*A Posteriori Error Majorant for Elliptic Partial Differential Equations with Complicated Coefficients*

**Presenter:**Stefan Sauter, Institut für Mathematik, Universität Zürich

*Room 750*

**Organisers:**Bruno Després (University Paris 6 (UPMC, Sorbonne University)), Lise-Marie Imbert-Gérard (University of Maryland), Peter Monk (University of Delaware), Hélène Barucq (Inria/France), Anouk Nicolopoulos (University Paris 6 (UPMC, Sorbonne University)), Martin Campos-Pinto (CNRS (LJLL-UPMC, Sorbonne University)), Guillaume Morel (CEA/UPMC), Ahmed Ratnani (Max-Planck IPP)

*Polynomial Trefftz-DG Method for Space-Time Elasto-Acoustics*

**Presenter:**Elvira Shishenina, Inria, Total S.A.

*Generalized Plane Waves for the convected Helmholtz equation*

**Presenter:**Lise-Marie Imbert-Gérard, University of Maryland

*A Stable Formulation of Resonant Maxwell's Equations in Cold Plasma*

**Presenter:**Anouk Nicolopoulos, University Paris 6 (UPMC, Sorbonne University)

*Structure-Preserving discretizations of the Maxwell system with discontinuous splines*

**Presenter:**Martin Campos Pinto, CNRS, Sorbonne Université

*Room 751*

**Organisers:**Jae-Hun Jung (SUNY Buffalo, Ajou University), Wai-Sun Don (School of Mathematical Sciences, Ocean University of China)

*Enhanced Robustness of Hybrid Compact-WENO Finite Difference Scheme for Hyperbolic Conservation Laws with Multi-resolution Analysis and Tukey's Boxplot Method*

**Presenter:**Zhen Gao, Ocean University of China

*Hybrid compact-WENO finite difference scheme with radial basis function based shock detection method for hyperbolic conservation laws*

**Presenter:**Wai-Sun Don, Ocean University of China

*RBF-WENO hybrid method and monotone edge detection method*

**Presenter:**Jae-Hun Jung, SUNY Buffalo, Ajou University

*Total variation bounded high order finite difference methods for one-dimensional conservation laws*

**Presenter:**Zhengfu Xu, Michigan Technological University

*Main Foyer*

*Room 200*

**Chair:**David Moxey (College of Engineering, Mathematics and Physical Sciences; University of Exeter)

Download to calendar

**Organisers:**David Moxey (University of Exeter), Joaquim Peiró (Imperial College London)

*Recent Advances in High-Order Mesh Generation at Pointwise*

**Presenter:**Steve L. Karman, Pointwise, Inc.

*High-order mesh operations based on a linear elasticity model*

**Presenter:**Rémi Feuillet, INRIA

*Mesh Generation Without De-featuring*

**Presenter:**Ruben Sevilla, Swansea University

*Imposing weak boundary conditions for mesh curving*

**Presenter:**Eloi Ruiz-Gironés, Barcelona Supercomputing Center - BSC

*Room 300*

**Organisers:**Oscar P. Bruno (Caltech, Pasadena CA), Catalin Turc (New Jersey Institute of Technology)

*Boundary Integral Equations of the Second Kind for Multi-Domain Transmission Problems.*

**Presenter:**Xavier Claeys, Sorbonne Université; INRIA, Alpines

*Wavenumber-explicit bounds for obstacle scattering with trapping, and application to boundary integral equation methods*

**Presenter:**Simon Chandler-Wilde, University of Reading

*Novel Integral Equation Scattering Solver, with Applications to Open-Waveguide Problems via the Windowed Green Function Method*

**Presenter:**Emmanuel Garza, California Institute of Technology

*High-order time domain boundary elements for screen problems*

**Presenter:**Heiko Gimperlein, Heriot-Watt University

*Room 309*

*Efficient geometric multigrid methods for discontinuous Galerkin discretizations*

**Presenter:**Daniel Fortunato, Harvard University

*Linearly scaling block smoothers for spectral element formulations*

**Presenter:**Immo Huismann, TU Dresden

*Preconditioning the Mass Matrix for High Order Polynomial Approximation*

**Presenter:**Shuai Jiang, Brown University

*Efficient solvers and tensor-product preconditioners for the implicit time integration of discontinuous Galerkin methods*

**Presenter:**Will Pazner, Brown University, UC Berkeley

*“Hybrid discontinuous Galerkin discretisation and domain decomposition preconditioners for the Stokes problem”*

**Presenter:**Victorita Dolean, University of Strathclyde, University Cote d'Azur

*A Preconditioned Iterative Spectral-Galerkin Scheme for Fast Nonlinear PDE-constrained Optimization*

**Presenter:**Lasse Hjuler Christiansen, Technical University of Denmark

*Room 640*

**Organisers:**Simona Perotto (Politecnico di Milano), Annalisa Quaini (University of Houston), Gianluigi Rozza (Scuola Internazionale Superiore di Studi Avanzati)

*Advanced isogeometric modeling of fluid-structure interaction problems*

**Presenter:**Alessandro Reali, Universiry of Pavia; Institute for Advanced Study, Technical University of Munich

*Topology Optimization: Towards CFD Modeling*

**Presenter:**Nicola Ferro, Politecnico di Milano, MOX

*Isogeometric Hierarchical Model Reduction with Stabilization for Advection-Dominated Problems*

**Presenter:**Yves Antonio Brandes Costa Barbosa, Politecnico di Milano

*Room 650*

**Organisers:**Tao Tang (Southern University of Science and Technology), Tao Zhou (Chinese Academy of Sciences)

*Exponential time differencing schemes for nonlocal Allen-Cahn equations*

**Presenter:**Zhonghua Qiao, The Hong Kong Polytechnic University

*Efficient Second Order Energy Stable Schemes for Phase-Field Equations*

**Presenter:**Haijun Yu, Academy of Mathematics and Systems Science, CAS; School of Mathematical Science, University of Chinese Academy of Sciences

**Presenter:**Xinghui Zhong, Zhejiang University

*Uncertainty quantification for phase field models*

**Presenter:**Tao Zhou, Chinese Academy of Sciences

*Room 651*

*Unwrapping HDG's dissipation characteristics for viscous problems*

**Presenter:**Rodrigo C. Moura, Technological Institute of Aeronautics

*Effective SVV design for CG-based under-resolved DNS of transitional/turbulent flows at high Reynolds numbers*

**Presenter:**Rodrigo C. Moura, Technological Institute of Aeronautics

*Dispersion-dissipation Analysis for Advection Problems with Non-constant Coefficients: Applications to Discontinuous Galerkin Formulations*

**Presenter:**Gonzalo Rubio, ETSIAE-UPM (School of Aeronautics in Madrid)

*A family of HLL-type solvers for the generalized Riemann problem*

**Presenter:**Claus Goetz, University of Hamburg

*Hyperviscosity for Arbitrary Lagrangian-Eulerian Hydrodynamics*

**Presenter:**Andrew W. Cook, LLNL

*Room 664*

**Organisers:**Nail Yamaleev (Old Dominion University), Mark H. Carpenter (NASA Langley Research Center)

*An Entropy Stable Split Form Discontinuous Galerkin Method for the Compressible Navier- Stokes Equations on General Hexahedral Meshes*

**Presenter:**David Kopriva, The Florida State University, San Diego State University

*Structured and Unstructured Entropy-Stable High-Order Methods for Simulating High-Speed Compressible Turbulent Flows*

**Presenter:**Travis Fisher, Sandia National Laboratories

*An Entropy Stable h/p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property*

**Presenter:**Lucas Friedrich, University of Cologne

*H/P Adaptive Entropy Stable Methods for the Compressible Navier-Stokes Equations: Curvilinear Grids*

**Presenter:**Mark Carpenter, NASA Langley Research Center

*Room 750*

*Greedy kernel-based function approximation by VKOGA: convergence rates and applications.*

**Presenter:**Bernard Haasdonk, University of Stuttgart

*Kernel Methods for Center Manifold Reduction of Nonlinear ODEs*

**Presenter:**Boumediene Hamzi, AlFaisal University

*Stabilized Gaussian-RBF interpolation based on the Hermite generating function expansion*

**Presenter:**Anna Yurova, Max-Planck-Institut für Plasmaphysik; Technische Universität München, Zentrum Mathematik

*Greedy algorithms for approximation with matrix-valued kernels*

**Presenter:**Dominik Wittwar, University of Stuttgart

*The Radial Basis Functions Method Applied to Groundwater Flow and Solute Transport Models*

**Presenter:**Nadun Dissanayake, Michigan Technological University

*Room 751*

*Fast parallel solvers for a high order Discontinuous Galerkin method for the Poisson equation*

**Presenter:**Matthias Maischak, Brunel University

*A Parallel Implementation of a Hierarchical Spectral Solver for Variable Coefficient Elliptic Partial Differential Equations*

**Presenter:**Natalie N. Beams, Rice University

*Dedalus: A parallel spectral framework for multidimensional PDEs*

**Presenter:**Keaton J. Burns, Massachusetts Institute of Technology

*Accelerating an implicit solver for the Helmholtz equation across architectures*

**Presenter:**Jan Eichstaedt, Imperial College London

*Main Foyer*

*Main Foyer*

Regular Decompositions: Discrete, Boundary-Aware, and $p$-Stable

*Room 200*

**Chair:** Mark Ainsworth (Brown University)

Download to calendar

#### Abstract

The term Helmholtz-type decomposition of ${\mathbf{H}(\operatorname{\bf curl},\Omega)}$, $\Omega\subset\mathbb{R}^{3}$, refers to stable splittings of the form

$$ {\mathbf{H}(\operatorname{\bf curl},\Omega)} = ({H}^{1}(\Omega))^{3} + \operatorname{\bf grad} H^{1}(\Omega).$$

These splittings have become a key tool in both the theoretical and numerical analysis of spaces of $\operatorname{\bf curl}$-conforming vectorfields, related variational problems, and the corresponding finite element spaces (edge elements).

Their discrete counterparts provide stable splittings of piecewise polynomial finite element subspaces of ${\mathbf{H}(\operatorname{\bf curl},\Omega)}$ into (i) piecewise polynomial continuous vector fields on $\Omega$, (ii) gradients of piecewise polynomial continuous scalar finite element functions, and (iii) a "small'' remainder.

We show the existence of such decompositions for Nédélec's tetrahedral edge element spaces of any polynomial degree with stability depending only on the geometry of the domain and the shape regularity of the mesh. Our decompositions also respect homogeneous boundary conditions on a part of the boundary of $\Omega$. Key tools for our construction are continuous regular decompositions, projection-based interpolation, and quasi-interpolation with low regularity requirements.

*Room 200*

**Organisers:**David Moxey (University of Exeter), Joaquim Peiró (Imperial College London)

*Adaptive curvilinear meshing*

**Presenter:**Jean-Francois Remacle, Universite catholique de Louvain

*A new framework for curving structured boundary-layer meshes*

**Presenter:**Amaury Johnen, Université catholique de Louvain, Barcelona Supercomputing Center

*Parallel curved mesh subdivision*

**Presenter:**Xevi Roca, Barcelona Supercomputing Center

*Towards automatic high-order mesh generation for industrial geometries*

**Presenter:**David Moxey, University of Exeter

*Room 300*

*Resolution of the Runge Phenomenon with grids based on non Classical Polynomials*

**Presenter:**Bernard Shizgal, University of British Columbia

*Order Preserving Interpolation for Summation by Parts Operators at Non-Conforming Grid Interfaces*

**Presenter:**Martin Almquist, Stanford University

*High order summation-by-parts finite difference operators for reentrant corners*

**Presenter:**Jonatan Werpers, Uppsala University

*A provably stable high-order finite difference method for the time-dependent Schrödinger equation on deforming domains*

**Presenter:**Ylva Rydin, Uppsala University

*Room 640*

*Mesh adaptation in very high order discontinuous Galerkin method*

**Presenter:**Jan Jaskowiec, Cracow University of Technolgy

*Identifying Optimal Meshes for High-order Implicit Large-Eddy Simulation of Turbulent Boundary Layers Using Kriging Surrogate Models*

**Presenter:**Yoshiaki Abe, Imperial College London

*RP-Adaptation for Two-Dimensional Flow Simulations with Shocks*

**Presenter:**Julian Marcon, Imperial College London

*An Anisotropic p-Adaptation Multigrid Scheme for the Discontinuous Galerkin Spectral Element Method*

**Presenter:**Andrés Mauricio Rueda-Ramírez, Universidad Politécnica de Madrid

*Using The Flexibility of p Refinement in Flux Reconstruction for Optimal Simulation of Turbulent Flows*

**Presenter:**Vikram Singh, Technion - Israel Institute of Technology

*Room 650*

**Organisers:**Thomas Hagstrom (Southern Methodist University), Oscar Bruno (California Institute of Technology)

*High-order Upwind schemes for Wave Equations on Overlapping Grids*

**Presenter:**William D. Henshaw, Rensselaer Polytechnic Institute

*Fast spectral time-domain PDE solvers for complex structures: the Fourier-Continuation method*

**Presenter:**Oscar P. Bruno, Caltech

*Approaching Hyperbolic Systems through Maps and Tents*

**Presenter:**Jay Gopalakrishnan, Portland State University

*Time-Domain Integral-Equation Scattering Solvers via Fourier Splitting*

**Presenter:**Mark Lyon, University of New Hampshire

*Room 664*

**Organisers:**Nail Yamaleev (Old Dominion University), Mark H. Carpenter (NASA Langley Research Center)

*Can A Scheme For The Non-Linear Navier-Stokes Equations Simultaneously Be Convergent And High-Order Accurate?*

**Presenter:**Magnus Svärd, University of Bergen

*Boundary Conditions for Nonlinear Problems*

**Presenter:**Jan Nordström, Linköping University

*Entropy Stable Gas Dynamics on Staggered, Unstructured Grids*

**Presenter:**Jared Crean, Rensselaer Polytechnic Institute

*Entropy Stable Artificial Dissipation Based on the Brenner Regularization of the Navier-Stokes Equations*

**Presenter:**Nail Yamaleev, Old Dominion University

*Room 750*

**Chair:**Stefan Sauter (Institut für Mathematik, Universität Zürich; Universität Zürich)

Download to calendar

**Organisers:**Stefan Sauter (University of Zurich), Markus Melenk (TU Vienna)

*Why is high frequency Helmholtz equation difficult to solve?*

**Presenter:**Hongkai Zhao, UC Irvine

*Coupling Finite Elements and Auxiliary Sources*

**Presenter:**Ralf Hiptmair, ETH Zurich

*Domain-decomposition preconditioning for frequency-domain wave problems*

**Presenter:**Euan Spence, University of Bath

*High frequency behavior of corner singularties in Helmholtz problems*

**Presenter:**Théophile Chaumont-Frelet, BCAM

*Room 751*

**Organisers:**Jae-Hun Jung (SUNY Buffalo, Ajou University), Sigal Gottlieb (UMass Dartmouth)

*Model- and data-specific spectral quadrature rules for likelihood evaluations with noisy data*

**Presenter:**Scott Field, University of Massachusetts Dartmouth

*Numerical solutions of the ideal magnetohydrodynamics equations using central-upwind schemes with a multidimensional limiting process*

**Presenter:**Myungjoo Kang, Seoul National University

*Spectral element simulation for ion channel modeling with protein structure data*

**Presenter:**Misun Min, Argonne National Laboraotry

*Main Foyer*

Asymptotic Preserving Discontinuous Galerkin Methods

*Room 200*

**Chair:** Jan S. Hesthaven (École Polytechnique Fédérale de Lausanne)

Download to calendar

#### Abstract

Asymptotic preserving (AP) methods are numerical schemes that are designed to work uniformly with respect to different scales or regimes of a model as its parameter varies, while mimicking the asymptotic limit. In this talk, we will start with discontinuous Galerkin methods applied to some stationary linear transport equations, and then report on our developments in the design and analysis of AP methods for several time-dependent kinetic transport equations. These methods are based on reformulations of the equations and involve high order DG methods in space as well as suitably selected temporal discretizations.

*Room 200*

**Chair:**Misun Min (Argonne National Laboratory, Mathematics and Computer Science Division)

Download to calendar

**Organisers:**Misun Min (Argonne National Laboratory), Paul Fischer (University of Illinois, Argonne National Laboratory), Tzanio Kolev (Lawrence Livermore National Laboratory)

*Eﬃcient discretizations for exascale applications*

**Presenter:**Tzanio Kolev, Lawrence Livermore National laboratory

*Recent Developments in Spectral Element Methods for Turbulent Flows*

**Presenter:**Paul Fischer, University of Illinois

*Efficient High-Order Discretization with MFEM*

**Presenter:**Veselin Dobrev, Lawrence Livermore National Laboratory

*High-Order Accurate Scale-Resolving Simulations of Low-Pressure Turbine Linear Cascades using Python at Petascale*

**Presenter:**Peter E. Vincent, Imperial College London

*Room 300*

**Organisers:**Bryan Quaife (Florida State University), Travis Askham (University of Washington), Ludvig af Klinteberg (Simon Fraser University)

*A stable, kernel dependent FMM for fluid flow*

**Presenter:**Travis Askham, University of Washington

*Local analysis for close evaluation of layer potentials*

**Presenter:**Shilpa Khatri, University of California, Merced

*Leveraging Deep Learning Optimized Hardware For High Order Solvers*

**Presenter:**Alexander Heinecke, Intel Corporation

*Room 309*

**Organisers:**Francisco Pla (Departamento de Matemáticas, Facultad de Ciencias y Tecnologías Químicas, Universidad de Castilla-La Mancha, 13071 Ciudad Real)

*Spectral numerical schemes for time-dependent convection with viscosity dependent on temperature*

**Presenter:**Jezabel Curbelo, Universidad Autónoma de Madrid

*Adaptive high order Discontinuous Galerkin methods for geophysical scale problems part I: introduction and numerical results on model problems*

**Presenter:**Luca Bonaventura, Politecnico di Milano

*Effects of rotation and thermal gradients on the formation of single-eyed vortices and multiple vortices*

**Presenter:**María Cruz Navarro, Universidad de Castilla- La Mancha

*Adaptive high order Discontinuous Galerkin methods for geophysical scale problems part II: recent progresses in the development of an efficient parallel library*

**Presenter:**Giovanni Tumolo, OGS-ICTP

*Room 650*

**Organisers:**Thomas Hagstrom (Southern Methodist University), Oscar Bruno (California Institute of Technology)

*Long Time Stable Time Domain Integral Equations and their Discretization*

**Presenter:**Thomas Hagstrom, Southern Methodist University

*Hermite and dG methods for wave equations and their application to uncertain and inverse problems*

**Presenter:**Daniel Appelo, University of Colorado Boulder

*Discrete conservation in time-dependent wave problems*

**Presenter:**Marc Gerritsma, TU Delft

*Accuracy and Stability of Windowed Fourier Methods for Hyperbolic PDEs*

**Presenter:**Rodrigo Platte, Arizona State University

*Room 651*

**Organisers:**Jie Shen (Purdue University), Mohsen Zayernouri (Michigan State University)

*What Is the Fractional Laplacian?*

**Presenter:**Anna Lischke, Brown University

*Data-Infused Simulation and Analysis of Anomalous Transport*

**Presenter:**Mohsen Zayernouri, Michigan State University

*An efficient numerical method for solving fractional Laplacian equations*

**Presenter:**Jie Shen, Purdue University (West Lafayette, IN, US)

**Presenter:**Ke Chen, University of Liverpool

*Room 664*

*Fifth-order Finite-volume WENO on Cylindrical Grids: Flux Evaluation Using Riemann Solvers and Gas-kinetic Scheme*

**Presenter:**Mohammad Afzal Shadab, Hong Kong University of Science and Technology

*A New Adaptive Weighted Essentially Non-Oscillatory WENO-theta Scheme for Hyperbolic Conservation Laws*

**Presenter:**Thien Binh Nguyen, Monash University

*A Novel Eight-Order Diffusive Scheme for Unstructured Polyhedral Grids using the Weighted Least-Squares Method*

**Presenter:**Duarte M. S. Albuquerque, Instituto Superior Técnico, Universidade de Lisboa

*An accurate and robust finite volume scheme based on the spline interpolation for solving the Euler and Navier–Stokes equations on non-uniform curvilinear grids*

**Presenter:**QIUJU WANG, Institute of Applied Physics and Computational Mathematics

*High order well-balanced finite volume methods for the Euler equations with gravity*

**Presenter:**Matteo Semplice, Università di Torino

*Room 750*

**Organisers:**Stefan Sauter (University of Zurich), Markus Melenk (TU Vienna)

*Scalable 3D Helmholtz: what is the right algorithm?*

**Presenter:**Laurent Demanet, MIT

*Domain Decomposition Method for 3D Time Harmonic Maxwell's Equations*

**Presenter:**Patrick Joly, INRIA

*Wavenumber-explicit hp-FEM for Maxwell's Equations*

**Presenter:**Markus Melenk, TU Vienna

*High order Whitney forms: from theory to practice*

**Presenter:**Francesca Rapetti, Universite de la Cote Azur

*Room 751*

**Organisers:**Jae-Hun Jung (SUNY Buffalo, Ajou University), Sigal Gottlieb (UMass Dartmouth)

*High-dimensional quadrature rule design via statistical techniques*

**Presenter:**Akil Narayan, University of Utah

*Topological data analysis of 3D spectral approximations of vascular disease*

**Presenter:**Jae-Hun Jung, SUNY Buffalo, Ajou University

*Main Foyer*

*Room 200*

**Organisers:**Misun Min (Argonne National Laboratory), Paul Fischer (University of Illinois, Argonne National Laboratory), Tzanio Kolev (Lawrence Livermore National Laboratory)

*Fluxo: An open-source highly scalable Discontinuous Galerkin Spectral Element Method with efficient implementation of stable two-point fluxes*

**Presenter:**Florian Hindenlang, Max-Planck Institute for Plasma Physics

*Nektar++: Latest advancements for large-scale simulations on complex geometries*

**Presenter:**Chris Cantwell, Imperial College London

*The E3SM spectral element atmosphere model*

**Presenter:**Mark Taylor, Sandia National Labs

*Nonhydrostatic Atmospheric and Ocean Models using Continuous and Discontinuous Galerkin Methods*

**Presenter:**Frank Giraldo, Naval Postgraduate School

*Room 300*

**Organisers:**Bryan Quaife (Florida State University), Travis Askham (University of Washington), Ludvig af Klinteberg (Simon Fraser University)

*A Fast Integral Equation Method for the Navier-Stokes Equations in 2D*

**Presenter:**Ludvig af Klinteberg, Simon Fraser University

*A Highly Accurate Boundary Integral Equation Method for Simulating Surfactant-Covered Drops in 3D*

**Presenter:**Chiara Sorgentone, KTH Royal Institute of Technology

*An integral equation based method for computing magneto-hydrodynamic equilibrium*

**Presenter:**Dhairya Malhotra, New York University

*High-fidelity boundary element solutions on many-core devices with Bempp-cl*

**Presenter:**Timo Betcke, University College London

*Room 309*

*Towards robust Large Eddy Simulations for discontinuous Galerkin methods*

**Presenter:**Esteban Ferrer, ETSIAE-UPM (School of Aeronautics in Madrid)

*Application of High-Order Finite-Volume Scheme with Anisotropic AMR to Large Eddy Simulation of Turbulent Premixed Flames*

**Presenter:**Clinton P. T. Groth, University of Toronto

*Jet Noise Propagation Using a Spectral/hp DG Method Coupled with an LES Code*

**Presenter:**Vishal Saini, Loughborough University

*Spectral/hp methodology study for SVV-LES on an Ahmed Body*

**Presenter:**Filipe Fabian Buscariolo, Imperial College, USP

*Computational Assessments of Finite Difference and Flux Reconstruction Schemes for Implicit Large Eddy Simulations*

**Presenter:**Viktor Linders, Technion - Israel Institute of Technology

*High Fidelity Spectral/hp Element Methods for Turbomachinery*

**Presenter:**Andrea Cassinelli, Imperial College London

*Room 640*

**Organisers:**Yulong Xing (Ohio State University), Xiangxiong Zhang (Purdue University)

*Asymptotic Preserving Schemes for Euler Equations of Gas Dynamics and Shallow Water Equations with Coriolis Forces*

**Presenter:**Alexander Kurganov, Southern University of Science and Technology

*Low Mach number asymptotic preserving finite volume methods for the acoustic and the Euler equations in multiple space dimensions*

**Presenter:**Christian Klingenberg, Wuerzburg University

*Structure Preserving Numerical Methods for Hyperbolic Systems of Conservation and Balance Laws*

**Presenter:**Alina Chertock, North Carolina State University

*Second-order invariant domain preserving approximation of the Euler equations using convex limiting*

**Presenter:**Jean-Luc Guermond, Texas A&M

*Room 650*

**Chair:**Gustaaf Jacobs (Department of Aerospace Engineering and Engineering Mechanics, San Diego State University)

Download to calendar

**Organisers:**Gustaaf Jacobs (San Diego State University), Wai-Sun Don (School of Mathematical Sciences, Ocean University of China), David Kopriva (San Diego State University)

*Implicit positivity-preserving high order discontinuous Galerkin methods for conservation laws*

**Presenter:**Chi-Wang Shu, Brown University

*High Order Hybrid Compact-WENO Finite Difference Schemes for Hyperbolic Conservation Laws*

**Presenter:**Wai Sun Don, Ocean University of China

*Smoothness-Increasing and Accuracy Conserving (SIAC) filter for shock capturing with spectral methods*

**Presenter:**Gustaaf Jacobs, San Diego State University

*A high order WENO method for all-Mach Euler simulations*

**Presenter:**tao xiong, xiamen university

*Room 651*

**Organisers:**Henar Herrero (Universidad de Castilla-La Mancha), Juan Sánchez-Umbría (Universitat Politècnica de Catalunya)

*Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow*

**Presenter:**Laurette Tuckerman, CNRS

*Shear-induced oscillations of low-Prandtl-number fluids in thermal convection*

**Presenter:**Marta Net, UPC

*Doubly periodic vortex-wave solutions in an infinite shear flow*

**Presenter:**Hugh M. Blackburn, Monash University

*Instability of Bubbles in Partially Occluded Hele-Shaw Cells*

**Presenter:**Andrew L. Hazel, The University of Manchester

*Room 664*

**Organisers:**Daan Huybrechs (KU Leuven), Marcus Webb (KU Leuven, FWO Flanders)

*Orthogonal polynomials on algebraic curves and differential equations*

**Presenter:**Sheehan Olver, Imperial College

*Frames and numerical approximation*

**Presenter:**Daan Huybrechs, KU Leuven

*General Tensor Computations in Polar Coordinates*

**Presenter:**Geoff Vasil, University of Sydney

*Frames and spectral methods on complicated domains*

**Presenter:**Marcus Webb, KU Leuven, FWO Flanders

*Room 750*

**Organisers:**Ana Alonso Rodriguez (University of Trento), Francesca Rapetti (Université Cote Azur)

*High Order Finite Elements and Preconditioners in Electromagnetism*

**Presenter:**Marcella Bonazzoli, Inria, Sorbonne Université, Paris

*General order Virtual Elements for Magnetostatic problems*

**Presenter:**Franco Dassi, Università Milano Bicocca

*Dual Complex for Structure Preserving Isogeometric Methods*

**Presenter:**Rafael Vazquez, Ecole Polytechnique Federale de Lausanne, IMATI-CNR

*Auxiliary Space Preconditioners for Discontinuous Galerkin Discretizations of H(curl)-elliptic Problems*

**Presenter:**Cecilia Pagliantini, École Polytechnique Fédérale de Lausanne

*Room 751*

**Chair:**Otilio Rojas (Barcelona Supercomputing Center, Universidad Central de Venezuela)

Download to calendar

**Organisers:**Vianey Villamizar (Brigham Young University, Department of Mathematcis), Otilio Rojas (Barcelona Supercomputing Center, Department of Computer Applications in Science and Engineering)

*Local high order radiation boundary conditions with no auxiliary variables for high order discretizations of the 3D Helmholtz equation*

**Presenter:**Semyon Tsynkov, NC State University

*A Fourth Order Compact Scheme for the 3D Wave Equation with Variable Propagation Speed*

**Presenter:**Semyon Tsynkov, NC State University

**Presenter:**Sebastian Acosta, Texas Children's Hospital, Baylor College of Medicine

*Highly Accurate Wave Scattering Computation: Isogeometric Analysis Coupled with Local High Order ABC*

**Presenter:**Vianey Villamizar, Brigham Young University

*Drawing Room, 170 Queens Gate*

*Main Foyer*

Adaptive methods for the simulation of diffusion in complex geometries

*Room 200*

**Chair:** Christoph Schwab (ETH Zurich)

Download to calendar

#### Abstract

We will review the state of the art in integral equation methods for the solution of the heat equation in moving geometries. With suitable fast algorithms, such methods achieve optimal complexity and, in the homogeneous case, require the discretization of the space-time boundary alone. They achieve high order accuracy with suitable quadratures and are straightforward to implement adaptively in space-time. We will discuss applications to biophysical modeling, reaction-diffusion systems, and computational fluid dynamics.

*Room 200*

**Organisers:**Misun Min (Argonne National Laboratory), Paul Fischer (University of Illinois, Argonne National Laboratory), Tzanio Kolev (Lawrence Livermore National Laboratory)

*High-Performance Implementation of High-Order Discontinuous Galerkin Methods*

**Presenter:**Peter Bastian, Heidelberg University

*High-performance matrix-free finite element programming with the deal.II library*

**Presenter:**Martin Kronbichler, Technical University of Munich

*Low-order preconditioning of high-order triangular finite element methods*

**Presenter:**Tim Warburton, Virginia Tech

*On performance and portability for generic finite element interfaces*

**Presenter:**Jeremy Thompson, CU Boulder

*Room 300*

**Organisers:**Philipp Schlatter (KTH Royal Institute of Technology)

*Nonconforming elements in Nek5000: Stability and Implementation*

**Presenter:**Adam Peplinski, KTH Royal Institute of Technology

*Adjoint-based error estimators and adaptive refinement in Nek5000*

**Presenter:**Nicolas Offermans, KTH Royal Institute of Technology

*On a mixed CG-HDG formulation for high-order simulations*

**Presenter:**Martin Vymazal, Imperial College London

*Lossy Data Compression and its Effects on Wall-bounded Turbulence*

**Presenter:**Philipp Schlatter, KTH Royal Institute of Technology

*A minimally intrusive low-memory approach to resilience for existing transient solvers*

**Presenter:**Chris Cantwell, Imperial College London

*Room 640*

**Organisers:**Yulong Xing (Ohio State University), Xiangxiong Zhang (Purdue University)

*Physical-constraints-preserving schemes for special relativistic magnetohydrodynamic equations*

**Presenter:**Huazhong Tang, Peking University, Xiangtan University

*A fourth order accurate bound-preserving compact finite difference scheme for scalar convection diffusion equations*

**Presenter:**Hao Li, Purdue University

*High-order well-balanced FVM for Euler equations*

**Presenter:**Luc Grosheintz-Laval, ETH Zürich

*Accurate Front Velocities via New Space-Time Quadrature Rules*

**Presenter:**Leonie Riebesam, RWTH Aachen University

*Room 650*

**Organisers:**Gustaaf Jacobs (San Diego State University), Wai-Sun Don (School of Mathematical Sciences, Ocean University of China), David Kopriva (San Diego State University)

*On the Selection of Test Norms for the Discontinous Petrov-Galerkin Methods Through their Relation with Numerical Flux-Induced Stabilization*

**Presenter:**Philip Zwanenburg, McGill University

*Stability of Overintegration Methods for Nodal Discontinuous Galerkin Spectral Element Methods*

**Presenter:**David Kopriva, Florida State University, San Diego State University

*An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations*

**Presenter:**Marvin Bohm, Universität zu Köln

*Investigation and Optimization of Kinetic Energy Preserving Flux Formulations for LES*

**Presenter:**Thomas Bolemann, University of Stuttgart, University of Cologne

*Room 651*

**Organisers:**Henar Herrero (Universidad de Castilla-La Mancha), Juan Sánchez-Umbría (Universitat Politècnica de Catalunya)

*Reduced basis method for eigenfunctions in a Rayleigh-Bénard problem*

**Presenter:**Francisco Pla, Universidad de Castilla-La Mancha

*Stability of three dimensional convective flows in cylindrical geometries without SO2 symmetry.*

**Presenter:**Isabel Mercader Calvo, Universitat Politecnica de Catalunya

*Routes to Chaos from Axisymmetric Vertical Vortices in a Rotating Cylinder*

**Presenter:**Damián Castaño Torrijos, UCLM

*The stability of Couette Flows VLSM*

**Presenter:**Sergio Hoyas, Universitat Politècnica de València

*Rotating Waves in Spherical Geometry: Thermal Convection in Thin Rotating Shells and the Magnetized Spherical Couette System*

**Presenter:**Ferran Garcia Gonzalez, Helmholtz-Zentrum Dresden-Rossendorf, University of Amsterdam

*Room 664*

**Organisers:**Xiong Meng (Harbin Institute of Technology), Jennifer K. Ryan (University of East Anglia), Qiang Zhang (Nanjing University)

*Local error estimates of local discontinuous Galerkin method for convection-diffusion equations with outflow boundary layer*

**Presenter:**Qiang Zhang, Nanjing University

*Negative-Order Norm Estimates of Arbitrary Lagrangian-Eulerian Discontinuous Galerkin Method for Nonlinear Hyperbolic Conservation Laws*

**Presenter:**Yan Xu, University of Science and Technology of China

*Room 750*

**Organisers:**Ana Alonso Rodriguez (University of Trento), Francesca Rapetti (Université Cote Azur)

*Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions*

**Presenter:**Alexandre Ern, Ecole Nationale des Ponts et Chaussees, Inria Paris

*Tree techniques for high order electromagnetic potentials.*

**Presenter:**Ana Alonso Rodriguez, University of Trento

*Dealing algebraically with high order Whitney forms*

**Presenter:**Francesca Rapetti, Universite Cote Azur

*The Auxiliary Space Preconditioner in Four Dimensions*

**Presenter:**Jay Gopalakrishnan, Portland State University

*Room 751*

**Organisers:**Vianey Villamizar (Brigham Young University, Department of Mathematcis), Otilio Rojas (Barcelona Supercomputing Center, Department of Computer Applications in Science and Engineering)

*Mixed-Dimensional Modeling of Wave Problems using a Dirichlet-to-Neumann Coupling Technique*

**Presenter:**Yoav Ofir, Technion - Israel Institute of Technology