Sparselizard (MIT License, Copyright (C) 2017-2019

Alexandre Halbach) is a general,

**multiphysics, open source** C++ finite element library running on

**Linux**,

**Mac** and

**Windows**. It is user friendly, robust, fast and

**multithreaded**. It is used to design next generation microdevices and it is validated against analytical solutions, third party software and measurements of the fabricated devices. It can handle a general set of problems in

**3D, 2D and 1D** such as

**mechanical (elasticity, geometric nonlinearity, buckling, contact), fluid flow (laminar, creeping), acoustic, thermal, thermoacoustic, fluid-structure interaction, electric, magnetic, electromagnetic, piezoelectric, superconductor,... **
problems (provided in form of a weak formulation as detailed in this

wikipedia page
). Problems with several

**millions of unknowns in 3D** and several

**tens of millions of unknowns in 2D** have been solved

**within minutes** on up to 16 cores/32 threads. Some built-in geometry definition and meshing tools are also provided.
A working example that solves an electrostatic problem on a grounded 3D disk with electric volume charges can be found below:

int vol = 1, sur = 2; // Disk volume and boundary as set in ’disk.geo’
mesh mymesh("disk.msh");
field v("h1"); // Nodal shape functions for the electric potential
v.setorder(vol, 2); // Interpolation order 2 on the whole domain
v.setconstraint(sur, 0); // Force 0 V on the disk boundary
formulation elec; // Electrostatics with 1 nC/m^3 charge density
elec += integral(vol, -8.85e-12 * grad(dof(v)) * grad(tf(v)) + 1e-9 * tf(v));
solve(elec); // Generate, solve and save solution to field v
(-grad(v)).write(vol, "E.vtk"); // Write the electric field to ParaView format

The built-in geometry definition and mesher can be used for now for rather simple 2D or extruded 3D geometries. Meshes of complex geometries can be imported from the widely-used open-source

GMSH meshing software (.msh format), from Nastran (.nas format) or from

**various** other

**supported mesh formats** (see the mesh object in the documentation). Points, lines, triangles, quadrangles, tetrahedra, hexahedra, prisms or any combination thereof are accepted in the mesh.

**Element curvature** for an accurate representation of the geometry is supported. The result files output by
sparselizard are in .vtk (

**ParaView**) or .pos (GMSH) format.

The problems can be readily solved in time with a time-stepping resolution or with the natively supported multiharmonic
resolution method. In the latter case the steady-state solution of a time-periodic problem can be obtained
in a single step, for linear as well as for nonlinear problems.

The library comes with hierarchical high order shape functions so that high order interpolations can be
used with an interpolation order adapted to every unknown field and geometrical region.