Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces
From MaRDI portal
Publication:5005204
DOI10.1137/20M1358128MaRDI QIDQ5005204
Publication date: 9 August 2021
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.01996
anisotropic Sobolev spacesspace-time methodsdirect solversfast diagonalizationparabolic evolution problemsBartels-Stewart
Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Direct numerical methods for linear systems and matrix inversion (65F05)
Related Items
Exponential convergence of hp-time-stepping in space-time discretizations of parabolic PDES ⋮ Time‐continuous and time‐discontinuous space‐time finite elements for advection‐diffusion problems ⋮ Integral representations and quadrature schemes for the modified Hilbert transformation ⋮ Fast parallel solver for the space-time IgA-DG discretization of the diffusion equation
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
- Arbitrary dimension convection-diffusion schemes for space-time discretizations
- A survey on direct solvers for Galerkin methods
- Space-time finite element methods for parabolic problems
- Numerical solution of parabolic problems based on a weak space-time formulation
- A time-stepping DPG scheme for the heat equation
- Boundary integral operators for the heat equation
- A new finite element formulation for computational fluid dynamics. VIII. The Galerkin/least-squares method for advective-diffusive equations
- A preconditioning strategy for linear systems arising from nonsymmetric schemes in isogeometric analysis
- Coercive space-time finite element methods for initial boundary value problems
- A note on the efficient evaluation of a modified Hilbert transformation
- Space-time least-squares finite elements for parabolic equations
- An exact realization of a modified Hilbert transformation for space-time methods for parabolic evolution equations
- An efficient solver for space-time isogeometric Galerkin methods for parabolic problems
- Direct solution of partial difference equations by tensor product methods
- Stability of Petrov-Galerkin discretizations: application to the space-time weak formulation for parabolic evolution problems
- 50 Years of Time Parallel Time Integration
- Direct Methods for Sparse Matrices
- Space-time adaptive wavelet methods for parabolic evolution problems
- Computational Methods for Linear Matrix Equations
- 1. Space-time boundary element methods for the heat equation
- 7. Space-time finite element methods for parabolic evolution equations: discretization, a posteriori error estimation, adaptivity and solution
- Initial-Boundary Value Problems for Parabolic Equations
- Numerical Approximation Methods for Elliptic Boundary Value Problems
- A numerical evaluation of sparse direct solvers for the solution of large sparse symmetric linear systems of equations
- The Multifrontal Method for Sparse Matrix Solution: Theory and Practice
- Solution of the Sylvester matrix equation AXB T + CXD T = E
- Time-Parallel Iterative Solvers for Parabolic Evolution Equations
- Matrix Calculus, Kronecker Product and Tensor Product
- Stability of sparse space-time finite element discretizations of linear parabolic evolution equations
- Stability of Galerkin discretizations of a mixed space–time variational formulation of parabolic evolution equations
- Fast Direct Solvers for Elliptic PDEs
- Parallel and Robust Preconditioning for Space-Time Isogeometric Analysis of Parabolic Evolution Problems
- Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures
- Fractional Space-Time Variational Formulations of (Navier--) Stokes Equations
- Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
- An improved error bound for reduced basis approximation of linear parabolic problems
- Galerkin Finite Element Methods for Parabolic Problems
- A survey of direct methods for sparse linear systems
- Petrov–Galerkin space-time hp-approximation of parabolic equations in H1/2
