数值分析
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
This paper investigates the convergence properties of the upwind difference scheme for the Hamilton--Jacobi--Bellman (HJB) equation, a central partial differential equation in optimal control theory. First, assuming the existence of a…
We consider three common mathematical models for time-harmonic high frequency scattering: the Helmholtz equation in two and three spatial dimensions, a transverse magnetic problem in two dimensions, and Maxwell's equation in three…
This work provides a comparative assessment of several low-dissipation numerical schemes for hyperbolic conservation laws, highlighting their performance relative to the classical Harten-Lax-van Leer (HLL) schemes. The schemes under…
We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with initial data in the form of a modulated highly oscillatory exponential. In this regime of a small scaling parameter $\varepsilon$, the solution exhibits…
The random feature method (RFM) constructs approximation spaces by initializing features from generic distributions, which provides universal approximation properties to solve general partial differential equations. However, such standard…
We study Kaczmarz type methods to solve consistent linear matrix equations. We first present a block Kaczmarz (BK) method that employs a deterministic cyclic row selection strategy. Assuming that the associated coefficient matrix has full…
We present an adaptive Chebyshev-based Boundary Integral Equation (CBIE) solver for electromagnetic scattering from smooth perfect electric conductor (PEC) objects. The proposed approach eliminates manual parameter tuning by introducing (i)…
Extreme rainfall over the Indian monsoon region poses severe societal and infrastructural risks but remains difficult to predict at daily time scales due to stochastic convective triggering and multiscale atmospheric interactions. While…
According to Noether's theorem the presence of a continuous symmetry in a Hamiltonian systems is equivalent to the existence of a conserved quantity, yet these symmetries are not always explicitly enforced in data-driven models. There…
We propose a novel error analysis framework for scaled generalized Laguerre and generalized Hermite approximations.This framework can be regarded as an analogue of the Nyquist-Shannon sampling theorem: It characterizes the spatial and…
Simulating flow problems is at the core of many engineering applications but often requires high computational effort, especially when dealing with complex models. This work presents a novel approach for resolving flow problems using the…
The Ozaki-II scheme is an emulation method that leverages the Chinese Remainder Theorem to compute high-precision matrix multiplication via a sequence of low-precision matrix multiplications. In this scheme, the attainable numerical…
This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…
This work is concerned with the development of quasi-Trefftz methods for first-order differential systems. It focuses on discrete quasi-Trefftz spaces, starting from their definition and including the construction of corresponding bases…
We deal with accelerating the solution of a sequence of large linear systems solved by preconditioned conjugate gradient method (PCG). The sequence originates from time-stepping within a simulation of an unsteady incompressible flow. We…
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion-convection-reaction equations and boundary conditions of mixed type. Since neither conformity…
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…
The paper presents results on piecewise polynomial approximations of tensor product type in Sobolev-Slobodecki spaces by various interpolation and projection techniques, on error estimates for quadrature rules and projection operators based…