# Solver Articles and Tutorials

## Python FEM and Multiphysics Simulations with FEniCS and FEATool

FEniCS is a flexible and comprehensive finite element FEM and partial differential equation PDE modeling and simulation toolkit with Python and C++ interfaces along with many integrated solvers. As both FEATool and FEniCS discretize equations employing a weak finite element formulation it is quite straightforward to …

## Running Matlab FEM and Multiphysics Simulations in Parallel

When tasked with performing many finite element simulations, for example in optimization studies or performing parametric studies over several variables as described in the previous parametric simulation script tutorial, one can speed up the overall process significantly by performing the simulations in parallel. This …

## CFD Solver Benchmark - FeatFlow and FEATool

To evaluate the efficiency of the FeatFlow CFD solver one can use the now classic DFG flow over a cylinder CFD benchmark [1][2] for which very accurate reference solutions for drag, lift, and pressure difference have been established [3][4]. The model problem is set up and solved with identical grids and finite element …

## FeatFlow - Fast External CFD Solver Integration with FEATool

Continually making physics simulation easier, better, and more approachable, this post introduces FeatFlow, a very fast and efficient finite element FEM based computational fluid dynamics (CFD) solver for the incompressible Navier-Stokes equations. The FeatFlow solver interface is now available in FEATool Multiphysics, …

## Fortran, Julia, and Matlab FEM Benchmark Comparison

Continuing the previous solver and assembly FEM benchmark comparison this followup ensures that identical simulation problem setup is compared, in this case a 2D Poisson problem solved on a unit square. The problem is discretized with Q1 bilinear Lagrange finite elements. Finite element functions such as assembly …

## FEM Assembly and Solver Benchmarks

It is both interesting and useful to compare simulation tools and the performance of different implementations. In the following we have performed three basic tests relevant to FEM simulation codes, sparse matrix vector multiplication, finite element matrix assembly, and solving the Poisson equation on a unit square, …