A new bounded cochain extension operator for differential forms on Lipschitz domains achieves global commutativity with the exterior derivative on the complement of harmonic forms and yields uniform Poincaré inequalities plus Neumann eigenvalue bounds on non-convex domains.
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Establishes equivalence of DEC cochains with generalized Whitney forms to prove convergence rates for the Hodge-Laplacian in full k-form generality on well-centered meshes.
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.
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Uniformly Bounded Cochain Extensions and Uniform Poincar\'e Inequalities
A new bounded cochain extension operator for differential forms on Lipschitz domains achieves global commutativity with the exterior derivative on the complement of harmonic forms and yields uniform Poincaré inequalities plus Neumann eigenvalue bounds on non-convex domains.
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A Framework for Analysis of DEC Approximations to Hodge-Laplacian Problems using Generalized Whitney Forms
Establishes equivalence of DEC cochains with generalized Whitney forms to prove convergence rates for the Hodge-Laplacian in full k-form generality on well-centered meshes.
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GPU Performance of an Entropy-Stable Discontinuous Galerkin Euler Solver with Non-Conservative Terms
GPU port of entropy-stable DG Euler solver with non-conservative buoyancy terms reaches nearly 70% of 64-bit peak on A100 volume kernels, delivers 10x speedup and 13x better energy efficiency versus CPU, and preserves symmetry-based flux savings.
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General Relativity via differential forms -- explorations in Plebanski's Formalism for GR
Plebanski's chiral 2-form formulation of GR reveals additional structure in Einstein's equations and supplies new analytical and numerical tools.