相关论文: Efficient variants of the CMRH method for solving …

This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems common in nonlinear partial differential equations (PDEs).…

The random feature method (RFM), a mesh-free machine learning-based framework, has emerged as a promising alternative for solving PDEs on complex domains. However, for large three-dimensional nonlinear problems, attaining high accuracy…

In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…

We consider scalar semilinear elliptic PDEs, where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem, we employ a damped Zarantonello iteration, which leads to…

In this paper, we propose a novel, computationally efficient reduced order method to solve linear parabolic inverse source problems. Our approach provides accurate numerical solutions without relying on specific training data. The forward…

We propose two variants of the Primal Dual Hybrid Gradient (PDHG) algorithm for saddle point problems with block decomposable duals, hereafter called Multi-Timescale PDHG (MT-PDHG) and its accelerated variant (AMT-PDHG). Through novel…

We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…

We develop a mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs. The efficiency of the proposed method is built upon four essential components: (i) a…

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

The full history recursive multilevel Picard approximation method for semilinear parabolic partial differential equations (PDEs) is the only method which provably overcomes the curse of dimensionality for general time horizons if the…

We consider coordinate descent (CD) methods with exact line search on convex quadratic problems. Our main focus is to study the performance of the CD method that use random permutations in each epoch and compare it to the performance of the…

This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…

This paper deals with the Hessian discretisation method (HDM) for fourth order semi-linear elliptic equations with a trilinear nonlinearity. The HDM provides a generic framework for the convergence analysis of several numerical methods,…

In this paper we consider some non-stationary relaxed synchronous and asynchronous multi-splitting methods for solving the linear complementarity problems with their coefficient matrices being H-matrices. The convergence theorems of the…

High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to low-order, matrix-based simulations, in particular in porous…

We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…

We propose an easy-to-implement iterative method for resolving the implicit (or semi-implicit) schemes arising in solving reaction-diffusion (RD) type equations. We formulate the nonlinear time implicit scheme as a min-max saddle point…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…