Related papers: Efficient flexible boundary conditions for long di…
Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…
In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the…
In this paper, we mainly focus on solving high-dimensional stochastic Hamiltonian systems with boundary condition, which is essentially a Forward Backward Stochastic Differential Equation (FBSDE in short), and propose a novel method from…
The variational principle serves as a fundamental framework for describing equilibrium states of physical systems via the minimization or extremization of an energy-like functional. While quantum algorithms have demonstrated promising…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…
Control-based continuation (CBC) is an experimental method that can reveal stable and unstable dynamics of physical systems. It extends the path-following principles of numerical continuation to experiments, and provides systematic…
This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D lattice-structured and periodic systems. The set of localized…
The U.S. power grid is undergoing a major paradigm shift with the increased development of renewable generators, electric vehicles, and data centers. In response to this growing need, the U.S. has ramped up the construction of…
This paper proposes a temporal two-grid compact difference (TTCD) scheme for solving the Benjamin-Bona-Mahony-Burgers (BBMB) equation with initial and periodic boundary conditions. The method consists of three main steps: first, solving a…
Boundary-condition (BC) handling is a major source of complexity in PDE solvers on structured and block-structured grids, especially for high-order methods and distributed-memory execution. We present Mat2Boundary, a DSL and compiler for…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
In this paper we develop a stochastic boundary conditions (SBC) for event-driven molecular dynamics simulations of a finite volume embedded within an infinite environment. In this method, we first collect the statistics of…
The Finite Difference (FD) and the Spectral Boundary Integral (SBI) methods have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. In this paper, we propose a new…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
Decomposition plays a significant role in cooperative co-evolution which shows great potential in large scale black-box optimization. However, current popular decomposition algorithms generally require to sample and evaluate a large number…
A new search algorithm for solving distributed constraint optimization problems (DisCOPs) is presented. Agents assign variables sequentially and compute bounds on partial assignments asynchronously. The asynchronous bounds computation is…
We introduce a general and fast convolution-based method (FCBM) for peridynamics (PD). Expressing the PD integrals in terms of convolutions and computing them by fast Fourier transform (FFT), we reduce the computational complexity of PD…