数值分析
This paper is concerned with partial Joint SVD-type Block Diagonalization of several matrices so that the extracted diagonal parts collectively optimally assume part of the total mass of all given matrices. For that reason, it will be…
We study finite element approximations of elliptic and parabolic interface problems with discontinuous coefficients and nonlinear jump conditions. We introduce a scalar interface reduction in which the solution is decomposed into a…
We propose a local Legendre frame (LLF) method for function approximation from equispaced data on a finite interval. Motivated by the difficulty of stable high-order polynomial approximation at equispaced points, especially in the presence…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
This article provides a primer on the spectral representation of random fields via the Karhunen-Lo\`eve Expansion (KLE). The goal is to bridge the gap between the theoretical foundations of the KLE and its application in computational…
Simulating diffusion in heterogeneous media presents a significant computational challenge, as resolving microscopic physical scales traditionally demands excessively fine computational grids. To overcome this barrier, we extend the…
We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or…
We investigate the use of randomized quasi-Monte Carlo (RQMC) in walk on spheres algorithms to solve boundary value problems for functions with Dirichlet boundary conditions in $\mathbb{R}^d$. For harmonic functions with $d=2$, the…
We propose a novel Krylov subspace method for estimating the finite impulse response (FIR) of a one-dimensional linear time-invariant systems. The method approximates the system's FIR using a kernel-based formulation combined with…
The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, the location/values of the applied Dirichlet/Neumann boundary…
This paper studies the time-dependent test-function error in the characteristic Galerkin-type semi-Lagrangian discontinuous finite element (CSLDG) method caused by numerical integration errors of the characteristic ODE solver, and its…
In this work, we report a stable ordered structure -- the cubic FDDD phase -- that has not previously been identified in the Landau-Brazovskii (LB) model, a fundamental and important model for studying crystals and their phase transitions.…
Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusions…
We develop a structure-preserving ADMM method, denoted SP-ADMM, for learning energy-stable spatial derivative stencils for Maxwell equations from noisy data. Starting from the source-free Maxwell system, we focus on a one-dimensional…
We propose two new alternative numerical schemes to solve the coupled Einstein-Euler equations in the Generalized Harmonic formulation. The first one is a finite difference (FD) Central Weighted Essentially Non-Oscillatory (CWENO) scheme on…
The efficient numerical solution of fractional differential equations has been recently tackled through the definition of Fractional HBVMs (FHBVMs), a class of Runge-Kutta type methods. Corresponding Matlab (c) codes have been also made…
The explicit two-stage fourth-order (TSFO) temporal-spatial coupling method is efficient and compact but suffers severe time-step restrictions for stiff problems with multiple scales. To address Professor Jiequan Li's call for an implicit…
Using the largest principal angle as a distance between same-dimensional linear subspaces of $\mathbb{R}^n$, we construct $k$-dimensional subspaces which deviate from every coordinate $k$-subspace by at least $\arccos(1/\sqrt n)$. The…
A procedure is presented to estimate the diffusion coefficient of a uniform patch of argon gas in a uniform background of helium gas. Molecular Dynamics (MD) simulations of the two gases interacting through the Lennard-Jones potential are…
This paper presents multilevel hybrid transport (MLHT) methods for solving the neutral-particle Boltzmann transport equation. The proposed MLHT methods are formulated on a sequence of spatial grids using a multilevel Monte Carlo (MLMC)…