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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Introduces the first massively parallel DEC library for 3D elliptic boundary value problems and demonstrates its application to thermal conductivity in cracked solids.
The authors extend Forman's combinatorial differential forms with operators for scalar variables to enable intrinsic, dimension-dependent modeling of diffusion in discrete complexes.
A discrete exterior calculus formulation of linear elasticity on cell complexes with displacements as primal 0-cochains and validation on classical analytic problems.
citing papers explorer
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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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Parallelized Discrete Exterior Calculus for Three-Dimensional Elliptic Problems
Introduces the first massively parallel DEC library for 3D elliptic boundary value problems and demonstrates its application to thermal conductivity in cracked solids.
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Diffusion in multi-dimensional solids using Forman's combinatorial differential forms
The authors extend Forman's combinatorial differential forms with operators for scalar variables to enable intrinsic, dimension-dependent modeling of diffusion in discrete complexes.
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A Geometric Formulation of Linear Elasticity Based on Discrete Exterior Calculus
A discrete exterior calculus formulation of linear elasticity on cell complexes with displacements as primal 0-cochains and validation on classical analytic problems.