相关论文: Parallel-in-time Multilevel Krylov Methods: A Prot…

We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…

In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge-Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems,…

Our goal is to present an elementary approach to the analysis and programming of sparse grid finite element methods. This family of schemes can compute accurate solutions to partial differential equations, but using far fewer degrees of…

A concise Matlab implementation of a stable parallelizable space-time Petrov-Galerkin discretization for parabolic evolution equations is given. Emphasis is on reusability of spatial finite element codes.

We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially non-oscillatory (WENO)…

We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the structure and Eulerian variables to describe the fluid. Explicit time stepping schemes for the IB method require…

This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…

We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…

In this work, we present a new high order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the…

The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…

The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…

Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…

In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) discontinuous Galerkin (DG) methods for simulating scalar wave equations in second order form in space. The two key ingredients of the schemes…

As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…

The multigroup neutron transport equations have been widely used to study the motion of neutrons and their interactions with the background materials. Numerical simulation of the multigroup neutron transport equations is computationally…

Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations.…

We present a GPU-accelerated version of a high-order discontinuous Galerkin discretization of the unsteady incompressible Navier-Stokes equations. The equations are discretized in time using a semi-implicit scheme with explicit treatment of…

This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in…