Numerical Method for Integrating Functions on Submanifolds of Euclidean Space or Compact Riemannian Manifolds
This paper presents a numerical method for computing the integral of a function over compact submanifolds in Euclidean space or compact Riemannian manifolds, using a digital representation of the "volume element" and a discretization of the integral.
Analytic Continuation of Solutions to the Helmholtz Equation with Dirichlet Boundary Conditions in Perturbed Half-Spaces
Solutions to the Helmholtz equation with Dirichlet boundary conditions in compactly perturbed half-spaces admit analytic continuations into specific regions of the complex plane, allowing for efficient numerical discretization.
A Highly Accurate Modified Laplace-Fourier Method for Solving Linear Neutral Delay Differential Equations
A new modified Laplace-Fourier method is developed that significantly improves the accuracy of solutions for linear neutral delay differential equations compared to the pure Laplace and original Laplace-Fourier methods.
An Energy Stable High-Order Discontinuous Galerkin Method with State Redistribution for Wave Propagation on Cut Meshes
The authors present a provably energy stable high-order discontinuous Galerkin (DG) method for solving the acoustic wave equation on cut meshes. They pair the DG scheme with state redistribution, a technique to address the small cell problem on cut meshes, and prove that the resulting scheme remains energy stable.
A Uniform Non-Linear Subdivision Scheme for Reproducing Polynomials on Non-Uniform Grids
The proposed subdivision scheme can reproduce second-degree polynomials on a variety of non-uniform grids without requiring prior knowledge of the grid specifics.
Optimal Convergence of an Adaptive Finite Element Method for Elastoplasticity
The paper proves that an adaptive finite element method for the primal problem of elastoplasticity with isotropic and linear kinematic hardening satisfies the axioms of adaptivity, which guarantees optimal convergence of the scheme.
An Implicit and Higher Order Time Discretization Scheme for Efficiently Solving Maxwell's Equations
This work presents a generalization of the authors' previous implicit leapfrog scheme to an arbitrary (even) order accurate time discretization method for efficiently solving the system of Maxwell's equations.
Efficient Matrix-Free Geometric Multigrid Preconditioning for Solving Phase-Field Fracture Problems with Local Mesh Refinement
This work presents an efficient matrix-free geometric multigrid preconditioner for solving the linear systems arising in the nonlinear solution of quasi-static phase-field fracture problems with local mesh refinement.
Efficient Adaptive Finite Element Method for Elliptic Eigenvalue Optimization with Phase-Field Approach
The authors propose an adaptive finite element method (AFEM) for efficiently solving an elliptic eigenvalue optimization problem using a phase-field approach. The AFEM incorporates adaptive mesh refinement based on a posteriori error estimators to improve the accuracy and computational efficiency compared to uniform mesh refinement.
Efficiency of Parallel Spectral Deferred Corrections
Efficiently optimizing parallel Spectral Deferred Corrections is crucial for computational efficiency.
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