Sparselizard (GNU GPLv2+, Copyright (C) 2020-2021

A. Halbach, Copyright (C) 2018-2019 A. Halbach, IMEC, Copyright (C) 2017 A. Halbach and C. Geuzaine, University of Liege) is an efficient, multiphysics, hp-adaptive, open source C++ finite element library running on Linux, Mac and Windows. It is used to design next generation microdevices (ultrasound transducers, micromirrors, microvalves, comb drives,...) and it is carefully

**validated** against analytical solutions, third party software and measurements of the fabricated devices. Efficient conformal adaptive mesh refinement (

**AMR**) is provided for 3D, 2D and 1D problems. A

**fast algorithm for mesh-to-mesh interpolation** and a general implementation of the

**mortar finite element method** allow to easily work with non-matching meshes and provide general periodic conditions.
Sparselizard can handle a general set of problems in

**3D, 2D axisymmetric, 2D and 1D** such as mechanical (anisotropic elasticity, geometric nonlinearity, buckling, contact, crystal orientation), fluid flow (laminar, creeping, incompressible, compressible), stabilized advection-diffusion, nonlinear acoustic, thermal, thermoacoustic, fluid-structure interaction, electric, magnetic, electromagnetic, piezoelectric, superconductor,...
problems with a

**transient, (multi)harmonic or damped/undamped eigenmode** analysis. A massive amount of data can be stored for

**delayed, remote post-processing** thanks to the

**ultra compact .slz data format**. 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 32 cores/64 threads (see

report). 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 / .vtu / .pvd (

**ParaView**) or .pos (GMSH) format.
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 mesh element/geometrical region (p-adaptivity).