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Examples

Linear problems

Filename Comments (preconditioners, numerical schemes)
diffusion-2d-PETSc.edp Distributed LU/Cholesky, domain decomposition and multigrid methods
diffusion-2d-PETSc-complex.edp  
heat-2d-PETSc.edp Transient diffusion equation, same as above
diffusion-periodic-2d-PETSc.edp Periodic boundary conditions, multigrid methods
diffusion-periodic-balanced-2d-PETSc.edp Better load balancing than above example
diffusion-substructuring-2d-PETSc.edp Balancing Domain Decomposition with Constraints
diffusion-3d-PETSc.edp Three-dimensional problem, domain decomposition and multigrid methods
diffusion-mg-2d-PETSc.edp Geometric non-nested multigrid methods
diffusion-mg-3d-PETSc.edp Geometric nested multigrid methods
helmholtz-2d-PETSc-complex.edp Domain decomposition methods with optimized boundary conditions
helmholtz-mg-2d-PETSc-complex.edp Geometric multigrid methods
laplace-RT-2d-PETSc.edp Vectorial two-dimensional problem with a block preconditioner (fieldsplit)
laplace-adapt-3d-PETSc.edp Three-dimensional problem with h adaptivity, multigrid methods using Mmg
laplace-adapt-dist-3d-PETSc.edp Three-dimensional problem with fully-distributed h adaptivity using ParMmg
laplace-lagrange-PETSc.edp Laplace equation with constraints and a block preconditioner (fieldsplit)
elasticity-2d-PETSc.edp Vectorial problem, domain decomposition (GenEO) and multigrid methods
elasticity-3d-PETSc.edp  
stokes-2d-PETSc.edp Distributed LU/Cholesky
stokes-3d-PETSc.edp  
stokes-block-2d-PETSc.edp Stokes equation defined as a block system with four matrices (fieldsplit)
stokes-fieldsplit-2d-PETSc.edp Block preconditioner (fieldsplit)
stokes-fieldsplit-3d-PETSc.edp  
maxwell-2d-PETSc.edp Direct LU/Cholesky
maxwell-3d-PETSc.edp Multigrid method
maxwell-mg-3d-PETSc-complex.edp Two-grid preconditioner
helmholtz-3d-surf-PETSc-complex.edp BEM with hierarchical matrices from Htool on surfaces
helmholtz-3d-line-PETSc-complex.edp BEM with hierarchical matrices from Htool on lines
helmholtz-coupled-2d-PETSc-complex.edp FEM coupled with BEM in a MatNest using a block preconditioner (fieldsplit)
PtAP-2d-PETSc.edp Parallel interpolation on non-matching grids + P’ A P operation
restriction-2d-PETSc.edp Coupled problems with one being defined on a restriction of the mesh of the other

Nonlinear problems

Filename Comments (preconditioners, numerical schemes)
bratu-2d-PETSc.edp  
bratu-hpddm-2d-PETSc.edp GenEO with reused coarse spaces
newton-2d-PETSc.edp  
newton-adaptmesh-2d-PETSc.edp Newton method and h adaptivity
newton-vi-2d-PETSc.edp Newton method and a variational inequality
newton-vi-adaptmesh-2d-PETSc.edp Newton method, h adaptivity, and a variational inequality
elasticity-SNES-3d-PETSc.edp Linear elasiticty with a Newton method
neo-Hookean-2d-PETSc.edp Nonlinear elasticity
navier-stokes-2d-PETSc.edp Steady-state Navier–Stokes equation for linear stability analysis
natural-convection-fieldsplit-2d-PETSc.edp Newton method and h adaptivity
vi-2d-PETSc.edp Variational inequalities

Time steppers and optimizers

Filename Comments (preconditioners, numerical schemes)
advection-TS-2d-PETSc.edp Implicit and explicit schemes
heat-TS-2d-PETSc.edp  
heat-TS-RHS-2d-PETSc.edp  
minimal-surface-Tao-2d-PETSc.edp Minimal surface problem
orego-Tao-PETSc.edp  
toy-Tao-PETSc.edp  

Eigenvalue problems

Filename Comments (preconditioners, numerical schemes)
laplace-2d-SLEPc.edp  
laplace-spherical-harmonics-2d-SLEPc.edp  
laplace-torus-2d-SLEPc.edp  
schrodinger-axial-well-2d-SLEPc.edp  
schrodinger-harmonic-oscillator-1d-SLEPc.edp  
schrodinger-harmonic-oscillator-2d-SLEPc.edp  
schrodinger-square-well-1d-SLEPc.edp  
laplace-2d-SLEPc-complex.edp  
laplace-beltrami-3d-surf-SLEPc.edp Eigenvalue problem on a surface
laplace-beltrami-3d-line-SLEPc.edp Eigenvalue problem on a curve
navier-stokes-2d-SLEPc-complex.edp Linear stability analysis of Navier–Stokes equations
stokes-2d-SLEPc.edp Inf-sup constant of Stokes equations
helmholtz-2d-SLEPc-complex.edp SVD of the discretized Helmholtz equation
mf-2d-SLEPc.edp Matrix-free SVD with user-provided matrix–vector and matrix transpose–vector multiplications
nonlinear-2d-SLEPc-complex.edp Nonlinear eigenvalue problem Ax = sqrt(lambda)x

Miscellaneous

Filename Comments (preconditioners, numerical schemes)
transpose-solve-PETSc.edp Solving a transposed system
Schur-complement-PETSc.edp Computing an exact Schur complement
block-PETSc.edp  
buildRecursive.edp Recursive mesh partitioning (for geometric multigrid)
withPartitioning.edp Connectivity construction with a user-supplied partitioning
createPartition.edp Creation of different partitions of unity using the same DD
save-load-Dmesh.edp Saving and loading a distributed mesh for restarting a computation
transfer.edp Parallel interpolation of finite element functions
reconstructDmesh.edp Construction of a distributed mesh from sequential nonoverlapping meshes
distributed-parmmg.edp Distributed ParMmg interface for mesh adaptation
redistributeDmesh.edp Gather and scatter a Dmesh on different MPI communicators
DMPlex-PETSc.edp Load and partition a mesh using a DM in two and three dimensions
function-PETSc.edp Custom plugin showing how to directly access PETSc in C++
convect.edp Calling the convert FreeFEM function on a distributed mesh
MatLoad-PETSc.edp Loading a distributed matrix/vector with various formats
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