Computational Mathematics

insight - Computational Mathematics

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.

Efficient Adaptive Time Step Selection for Spectral Deferred Corrections

Efficient adaptive time step selection enhances computational efficiency in solving differential equations.

Residual Multi-Fidelity Neural Network Computing: Efficient Surrogate Modeling Using Multi-Fidelity Information

The author presents a residual multi-fidelity computational framework for constructing efficient neural network surrogates using multi-fidelity information.

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