Manifolds, tensor analysis, and applications: 2nd edition
Manifolds, tensor analysis, and applications: 2nd edition
Covolume Solutions of Three-Dimensional Div-Curl Equations
SIAM Journal on Numerical Analysis
A staggered-grid multidomain spectral method for the compressible Navier-Stokes equations
Journal of Computational Physics
Spectral methods in MatLab
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Journal of Computational Physics
Discrete Calculus: Applied Analysis on Graphs for Computational Science
Discrete Calculus: Applied Analysis on Graphs for Computational Science
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
Discrete Lie Advection of Differential Forms
Foundations of Computational Mathematics
Foundations of Computational Mathematics
Journal of Computational Physics
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Preserving in the discrete realm the underlying geometric, topological, and algebraic structures at stake in partial differential equations has proven to be a fruitful guiding principle for numerical methods in a variety of fields such as elasticity, electromagnetism, or fluid mechanics. However, structure-preserving methods have traditionally used spaces of piecewise polynomial basis functions for differential forms. Yet, in many problems where solutions are smoothly varying in space, a spectral numerical treatment is called for. In an effort to provide structure-preserving numerical tools with spectral accuracy on logically rectangular grids over periodic or bounded domains, we present a spectral extension of the discrete exterior calculus (DEC), with resulting computational tools extending well-known collocation-based spectral methods. Its efficient implementation using fast Fourier transforms is provided as well.