Examples
Linear problems
Filename |
Comments (preconditioners, numerical schemes) |
|---|---|
Distributed LU/Cholesky, domain decomposition and multigrid methods |
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Transient diffusion equation, same as above |
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Periodic boundary conditions, multigrid methods |
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Better load balancing than above example |
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Balancing Domain Decomposition with Constraints |
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Three-dimensional problem, domain decomposition and multigrid methods |
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Geometric non-nested multigrid methods |
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Geometric nested multigrid methods |
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Domain decomposition methods with optimized boundary conditions |
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Geometric multigrid methods |
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Vectorial two-dimensional problem with a block preconditioner (fieldsplit) |
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Vectorial three-dimensional problem with a block preconditioner (fieldsplit) |
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Three-dimensional problem with h adaptivity, multigrid methods using Mmg |
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Three-dimensional problem with fully-distributed h adaptivity using ParMmg |
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Laplace equation with constraints and a block preconditioner (fieldsplit) |
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Vectorial problem, domain decomposition (GenEO) and multigrid methods |
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Domain decomposition (GenEO for saddle-point problems) |
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Distributed LU/Cholesky |
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Stokes equation defined as a block system with four matrices (fieldsplit) |
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Block preconditioner (fieldsplit) |
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Domain decomposition (GenEO for saddle-point problems) |
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Oseen problem preconditioned by Pressure Convection–Diffusion (PCD) |
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Direct LU/Cholesky |
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Multigrid method |
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Two-grid preconditioner |
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BEM with hierarchical matrices from Htool on surfaces |
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BEM with hierarchical matrices from Htool on lines |
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FEM coupled with BEM in a MatNest using a block preconditioner (fieldsplit) |
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Parallel interpolation on non-matching grids + P’ A P operation |
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Coupled problems with one being defined on a restriction of the mesh of the other |
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Bilaplacian using Morley finite element |
Nonlinear problems
Filename |
Comments (preconditioners, numerical schemes) |
|---|---|
GenEO with reused coarse spaces |
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Newton method and h adaptivity |
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Newton method and a variational inequality |
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Newton method, h adaptivity, and a variational inequality |
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Linear elasiticty with a Newton method |
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Nonlinear elasticity |
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Steady-state Navier–Stokes equation for linear stability analysis |
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Newton method and h adaptivity |
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Variational inequalities |
Time steppers and optimizers
Filename |
Comments (preconditioners, numerical schemes) |
|---|---|
Implicit and explicit schemes |
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Minimal surface problem |
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Eigenvalue problems
Filename |
Comments (preconditioners, numerical schemes) |
|---|---|
Eigenvalue problem on a surface |
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Eigenvalue problem on a curve |
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Linear stability analysis of Navier–Stokes equations |
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Inf-sup constant of Stokes equations |
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SVD of the discretized Helmholtz equation |
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Matrix-free SVD with user-provided matrix–vector and matrix transpose–vector multiplications |
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Nonlinear eigenvalue problem Ax = sqrt(lambda)x |
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Polynomial eigenvalue problem (A2 lambda^2 x + A1 lambda + A0)x = 0 |
Miscellaneous
Filename |
Comments (preconditioners, numerical schemes) |
|---|---|
Solving a transposed system |
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Computing an exact Schur complement |
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Recursive mesh partitioning (for geometric multigrid) |
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Connectivity construction with a user-supplied partitioning |
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Creation of different partitions of unity using the same DD |
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Saving and loading a distributed mesh for restarting a computation |
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Parallel interpolation of finite element functions |
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Construction of a distributed mesh from sequential nonoverlapping meshes |
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Distributed ParMmg interface for mesh adaptation |
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Gather and scatter a Dmesh on different MPI communicators |
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Load and partition a mesh using a DM in two and three dimensions |
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Custom plugin showing how to directly access PETSc in C++ |
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Calling the convert FreeFEM function on a distributed mesh |
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Loading a distributed matrix/vector with various formats |
Reproducible science
Article |
Source code |
|---|---|
Augmented Lagrangian preconditioner for large-scale hydrodynamic stability analysis |
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A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces |
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