相关论文: Total Variation Diminishing (TVD) method for Elast…

In this paper, we propose an adaptive finite difference scheme in order to numerically solve total variation type problems for image processing tasks. The automatic generation of the grid relies on indicators derived from a local estimation…

We develop a spectral low-mode reduced solver for second-order elliptic boundary value problems with spatially varying diffusion coefficients. The approach projects standard finite difference or finite element discretization onto a global…

Computing the electric eddy currents in non-linear materials, such as superconductors, is \E{not straightforward}. The design of superconducting magnets and power applications needs electromagnetic computer modeling, being in many cases a…

In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…

In this paper, we have solved 1D special relativistic hydrodynamical equations using different numerical method in computational gas dynamics. The numerical solutions of these equations for smooth wave cases give better solution when we use…

Application of current and near-term quantum hardware to the electronic structure problem is highly limited by qubit counts, coherence times, and gate fidelities. To address these restrictions within the variational quantum eigensolver…

In this paper, we construct a novel Eulerian-Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exact solutions to such problems may contain shocks though the…

This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…

The aim of this paper is twofold. On the one hand, we test numerically the performance of mixed virtual elements in three dimensions for the first time in the literature to solve the mixed formulation of three-dimensional elliptic equations…

We introduce a method-of-lines formulation of the closest point method, a numerical technique for solving partial differential equations (PDEs) defined on surfaces. This is an embedding method, which uses an implicit representation of the…

A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…

We propose in this paper a Proper Generalized Decomposition (PGD) approach for the solution of problems in linear elastodynamics. The novelty of the work lies in the development of weak formulations of the PGD problems based on the…

Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…

In this paper, we propose Total Variation Regularized Tensor-on-scalar Regression(TVTR), a novel method for estimating the association between a tensor outcome (a one dimensional or multidimensional array) and scalar predictors. While the…

We consider the initial situation where a dataset has been over-partitioned into $k$ clusters and seek a domain independent way to merge those initial clusters. We identify the total variation distance (TVD) as suitable for this goal. By…

Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…

We present a new meshless method for scalar diffusion equations which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of…

Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…

A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented.…

Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature. Existing solver-based acceleration methods often face image quality degradation…