Some of the most important geometric integrators for both ordinary and partial differential
equations are reviewed and illustrated with examples in mechanics. The class of …

We utilize generalized moving least squares (GMLS) to develop meshfree techniques for
discretizing hydrodynamic flow problems on manifolds. We use exterior calculus to formulate …

The formulation of combinatorial differential forms, proposed by Forman for analysis of
topological properties of discrete complexes, is extended by defining metric-dependent …

The quantized vortices in superfluids are modeled by the Gross-Pitaevskii equation whose
numerical time integration is instrumental in the physics studies of such systems. In this …

A spectral approach to building the exterior calculus in manifold learning problems is
developed. The spectral approach is shown to converge to the true exterior calculus in the …

The present work develops, verifies, and benchmarks a hybrid discrete exterior calculus and
finite difference (DEC-FD) method for density-stratified thermal convection in spherical …

We present a new hybrid discrete exterior calculus (DEC) and finite difference (FD) method
to simulate fully three-dimensional Boussinesq convection in spherical shells subject to …

The present work investigates granulation or convective flow patterns in density-stratified (or
anelastic) convection in spherical shells. The density-stratified thermal convection is typically …

Computational modeling is a key resource to gather insight into physical systems in modern
scientific research and engineering. While access to large amount of data has fueled the use …

A formulation of elliptic boundary value problems is used to develop the first discrete exterior
calculus (DEC) library for massively parallel computations with 3D domains. This can be …