相关论文: An Efficient Explicit-Implicit Adaptive Method for…

The E(xplicit)I(implicit)N(null) method was developed recently to remove numerical instability from PDEs, adding and subtracting an operator $\mathcal{D}$ of arbitrary structure, treating the operator implicitly in one case, and explicitly…

A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite difference method for solving parabolic equations, due…

We present a novel, fast differentiable simulator for soft-body learning and control applications. Existing differentiable soft-body simulators can be classified into two categories based on their time integration methods: Simulators using…

The DMD (Dynamic Mode Decomposition) method has attracted widespread attention as a representative modal-decomposition method and can build a predictive model. However, the DMD may give predicted results that deviate from physical reality…

This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More…

We introduce implicit Deep Adaptive Design (iDAD), a new method for performing adaptive experiments in real-time with implicit models. iDAD amortizes the cost of Bayesian optimal experimental design (BOED) by learning a design policy…

Affine Body Dynamics (ABD) within the Incremental Potential Contact (IPC) framework provides accurate simulation of extremely stiff solids exhibiting near-rigid behavior, with strict non-penetration guarantees. However, IPC's globally…

The Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions (PNP-FBV) describe ion transport with Faradaic reactions, and have applications in a number of fields. In this article, we develop an adaptive…

We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends…

In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…

Peridynamics formulates the balance of linear momentum as an integro-differential equation, making it naturally suited for fracture modeling without special treatment of discontinuities. The bond-associated correspondence formulation…

Simulating stiff materials in applications where deformations are either not significant or can safely be ignored is a pivotal task across fields. Rigid body modeling has thus long remained a fundamental tool and is, by far, the most…

This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…

Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…

Accurate prediction of damage and fracture evolution is critical for the safety design and preventive maintenance of engineering structures, however existing computational methods face significant limitations. On one hand, discrete damage…

Peridynamic (PD) theory is significant and promising in engineering and materials science; however, it imposes challenges owing to the enormous computational cost caused by its nonlocality. Our main contribution, which overcomes the…

Adaptive quasicontinuum (QC) methods are important methodologies in molecular mechanics for the simulations of materials with defects, intending to achieve the optimal balance of accuracy and efficiency on the fly. In this study, we propose…

Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…