In this article we describe a mesh generation toolchain for molecular modeling. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both surface (triangular) and volumetric (tetrahedral) meshes. Experiments on a number of molecules are demonstrated, showing that our toolchain possesses a number of desirable properties: feature-preservation, local adaptiv...

This paper describes an algorithm to implement image filtering and enhancement operations by processing adaptive triangular meshes that represent gray-level images. Experimental results show that these operations are significantly more efficient when they are performed upon triangular meshes than by sequentially processing all the pixels contained in the given images.

We introduce a novel spectral element method based on the ultraspherical and hierarchical Poincar\'{e}-Steklov scheme for solving second-order linear partial differential equations polygonal domains with unstructured quadrilateral or triangular meshes. Properties of lead to almost banded systems, allowing be competitive in high-polynomial regime ($p > 5$). The enables precomputed solution opera...

We present a new parallel repartitioning algorithm for adaptive finite-element meshes that significantly reduces the amount of data that needs to move between processors in order to rebalance a workload after mesh adaptation (refinement or coarsening). These results derive their importance from the fact that the time to migrate data can be a large fraction of the total time for the parallel ada...

The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11 6 -approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infinite triangular mesh is ...

This paper describes two approaches that allow us to intersect rays with triangular meshes more quickly by amortizing computation over neighbouring triangles. The first approach accomplishes this by performing the in-out test for each triangle using three plane equations, each one representing a boundary edge for the triangle. Each plane is shared between four neighbouring triangles and the cos...

We present a systematic procedure to improve the qualities of triangular molecular surface meshes and at the same time preserve the manifoldness. The procedure utilizes an algorithm to remove redundant points having three or four valences and another algorithm to smooth the mesh using a modified version of Laplacian method without causing intersecting triangles. This approach can be effectively...

We present a GPU-accelerated method for large scale, coupled incompressible fluid flow and heat transfer problems. A high-order, nodal discontinuous Galerkin is utilized to discretize governing equations on unstructured triangular meshes. semi-implicit scheme with explicit treatment of the advective terms implicit split Stokes operators are used time discretization. The pressure system solved c...