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Mathematics Group


Voro++: A Three-dimensional Voronoi Library in C++

Voro++ is an open source software library for the computation of the Voronoi diagram, a widely-used tessellation that has applications in many scientific fields. For a set of points in a domain, the tessellation is defined by associating a cell of space to each point, consisting of the part of the domain closer to that point than any other.  Several mature software libraries exist for computing the Voronoi tessellation (such as Qhull, used by MATLAB, and CGAL) but these typically compute the… Read More »

DistMesh: High-Quality Unstructured Mesh Generation for Implicit Geometries

DistMesh is a simple MATLAB code for generation of unstructured triangular and tetrahedral meshes. The geometries are specified by implicit functions, with negative sign inside the region and positive outside. DistMesh uses the Delaunay triangulation routine in MATLAB and tries to optimize the node locations by a force-based smoothing procedure. The topology is regularly updated by Delaunay. The boundary points are only allowed to move tangentially to the boundary by projections using the… Read More »

GMPFRXX: An integrated C++ Implementation of the GNU MP and MPFR Multiple-precision Libraries

Many important problems in scientific computing are extremely ill-conditioned, and require intermediate calculations to be done with many more digits of precision than the desired accuracy of the answer. Examples include resolving clusters of eigenvalues, designing numerical quadrature schemes for arbitrary families of functions, and computing asymptotic expansions of solutions of elliptic partial differential equations near corners (see the figure)). In such problems, it is desirable to write… Read More »