相关论文: pde2path - version 2.0: faster FEM, multi-paramete…

Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…

The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple…

We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely…

Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…

We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tangent spaces spanned by the nearest neighbors to compress…

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…

As integrated photonic systems grow in scale and complexity, Photonic Design Automation (PDA) tools and Process Design Kits (PDKs) have become increasingly important for layout and simulation. However, fixed PDKs often fail to meet the…

A new method for Ewald summation in planar/slablike geometry, i.e. systems where periodicity applies in two dimensions and the last dimension is "free" (2P), is presented. We employ a spectral representation in terms of both Fourier series…

In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…

The GooFit package provides physicists a simple, familiar syntax for manipulating probability density functions and performing fits, and is highly optimized for data analysis on NVIDIA GPUs and multithreaded CPU backends. GooFit was updated…

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…

Algorithms are presented for the tanh- and sech-methods, which lead to closed-form solutions of nonlinear ordinary and partial differential equations (ODEs and PDEs). New algorithms are given to find exact polynomial solutions of ODEs and…

This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory…

We present SymPhas 2.0, a major update of the compile-time symbolic algebra simulation framework SymPhas for phase-field and reaction-diffusion models. This release introduces significant expansions and enhancements that enable the…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

We introduce suitable coordinate systems for pipes and their variants that allow us to transform partial differential equations (PDEs) on the pipe surfaces or in the solid pipes into computational domains with fixed limits/ranges. Such a…

In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…

This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where the system exhibits multiple coexisting solutions for given…