Related papers: Parallel stochastic methods for PDE based grid gen…
Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid…
This paper presents a distributed memory method for anisotropic mesh adaptation that is designed to avoid the use of collective communication and global synchronization techniques. In the presented method, meshing functionality is separated…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
We propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based…
The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
Decentralized optimization is a promising parallel computation paradigm for large-scale data analytics and machine learning problems defined over a network of nodes. This paper is concerned with decentralized non-convex composite problems…
We present a geometric multigrid solver based on adaptive smoothed aggregation suitable for Discontinuous Galerkin (DG) discretisations. Mesh hierarchies are formed via domain decomposition techniques, and the method is applicable to fully…
In this paper, we propose a stochastic geometric iterative method to approximate the high-resolution 3D models by finite Loop subdivision surfaces. Given an input mesh as the fitting target, the initial control mesh is generated using the…
Multistage stochastic programming is a powerful tool allowing decision-makers to revise their decisions at each stage based on the realized uncertainty. However, in practice, organizations are not able to be fully flexible, as decisions…
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…
A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
A general method to generate a centrosymmetric matrix associated with the solving of partial differential equation (PDE) on an irreducible domain by means of a linear equation system is proposed. The method applies to any PDE for which both…
The resolution of the Shallow-water equations is of practical interest in the study of inundations and often requires very large and dense meshes to accurately simulate river flows. Those large meshes are often decomposed into multiple…
Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse…
The paper describes a sparse direct solver for the linear systems that arise from the discretization of an elliptic PDE on a two dimensional domain. The scheme decomposes the domain into thin subdomains, or ``slabs'' and uses a two-level…
We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle…