A simple GPU implementation of spectral-element methods for solving 3D Poisson type equations on rectangular domains and its applications
DOI10.4208/CICP.OA-2024-0072MaRDI QIDQ6670108
Jie Shen, Xiangxiong Zhang, Xin Yu Liu
Publication date: 22 January 2025
Published in: Communications in Computational Physics (Search for Journal in Brave)
direct solverrectangular domainGPUspectral element methods3D Poisson equationtensor matrix multiplication
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Parallel numerical computation (65Y05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Finite difference methods for boundary value problems involving PDEs (65N06) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical computation of matrix exponential and similar matrix functions (65F60)
Cites Work
- A GPU parallelized spectral method for elliptic equations in rectangular domains
- Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications
- Nodal discontinuous Galerkin methods on graphics processors
- Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries
- Fast direct Poisson solvers for high-order finite element discretizations in rectangularly decomposable domains
- The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
- Discrete maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation
- An efficient and accurate numerical method for the spectral fractional Laplacian equation
- Superconvergence of high order finite difference schemes based on variational formulation for elliptic equations
- An efficient direct parallel spectral-element solver for separable elliptic problems
- An overview of projection methods for incompressible flows
- Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
- Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Tensor product analysis of partial difference equations
- On the Convergence of Sobolev Gradient Flow for the Gross–Pitaevskii Eigenvalue Problem
- Positivity-preserving and energy-dissipative finite difference schemes for the Fokker–Planck and Keller–Segel equations
- Accuracy of Spectral Element Method for Wave, Parabolic, and Schrödinger Equations
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