An electrical engineering perspective on naturality in computational physics
DOI10.1007/s10444-024-10197-6MaRDI QIDQ6624471
Peter Robert Kotiuga, Valtteri Lahtinen
Publication date: 25 October 2024
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Differential complexes (58J10) Simplicial sets and complexes in algebraic topology (55U10) Chain complexes in algebraic topology (55U15) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Asymptotic analysis in optics and electromagnetic theory (78M35) Applications of differential geometry to engineering (53Z30)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces
- Why starting from differential equations for computational physics?
- The geometric realization of a semi-simplicial complex
- Cochain algebra on manifolds and convergence under refinement
- Difference forms
- Mixed finite elements in \(\mathbb{R}^3\)
- Sobolev spaces of differential forms and de Rham-Hodge isomorphism
- Hilbert complexes
- Natural differential operators on Riemannian manifolds and representations of the orthogonal and special orthogonal groups
- Analytic torsion and R-torsion of Riemannian manifolds
- An analysis of finite volume, finite element, and finite difference methods using some concepts from algebraic topology
- Lie theory for nilpotent \(L_{\infty}\)-algebras
- A Lefschetz fixed point formula for elliptic complexes. I
- Sur les théorèmes de de Rham
- Homotopical patch theory
- Dirichlet: His Life, His Principle, and His Problem
- Categorical Homotopy Theory
- Differential Forms and Boundary Integral Equations for Maxwell-Type Problems
- Electricity and Magnetism for Mathematicians
- Algebraic structures underneath geometric approaches
- Physics, Topology, Logic and Computation: A Rosetta Stone
- Categories for the Practising Physicist
- Missed opportunities
- Natural Operations on Differential Forms
- Finite element exterior calculus, homological techniques, and applications
- Finite element exterior calculus: from Hodge theory to numerical stability
- Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
- Natural Vector Bundles and Natural Differential Operators
- Finite-Difference Approach to the Hodge Theory of Harmonic Forms
- Higher Category Theory
- Canonical construction of finite elements
- Yee-like schemes on a tetrahedral mesh, with diagonal lumping
- Extrusion, contraction: their discretization via Whitney forms
- Categorical Generalization and Physical Structuralism
- Electromagnetic Theory and Computation
- From Euler, Ritz, and Galerkin to Modern Computing
- Categories in Control
- Hazelnut: a bidirectionally typed structure editor calculus
- Computational higher-dimensional type theory
- Homotopy Type Theory: Univalent Foundations of Mathematics
- The Mathematical Theory of Finite Element Methods
- Overdetermined systems of linear partial differential equations
- FREDHOLM COMPLEXES
- Univalence for inverse diagrams and homotopy canonicity
- The Geometric Basis of Numerical Methods
- Variational methods for the solution of problems of equilibrium and vibrations
- Algebraic \(K\)-theory
- Discrete Hodge operators
This page was built for publication: An electrical engineering perspective on naturality in computational physics
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6624471)