相关论文: High order difference schemes using the Local Anis…
Lax-Wendroff flux reconstruction (LWFR) schemes have high order of accuracy in both space and time despite having a single internal time step. Here, we design a Jacobian-free LWFR type scheme to solve the special relativistic hydrodynamics…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
Laser Powder Bed Fusion (LPBF) additive manufacturing has revolutionized industries with its capability to create intricate and customized components. The LPBF process uses moving heat sources to melt and solidify metal powders. The fast…
We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation…
Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least…
There has been an increasing interest in developing efficient immersed boundary method (IBM) based on Cartesian grids, recently in the context of high-order methods. IBM based on volume penalization is a robust and easy to implement method…
Solving partial differential equations (PDEs) on manifolds defined by randomly sampled point clouds is a challenging problem in scientific computing and has broad applications in various fields. In this paper, we develop a two-step…
This paper presents a novel and straightforward compact reconstruction procedure for the high-order finite volume method on unstructured grids. In this procedure, we constructed a linear approximation relationship between the mean values…
Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution of partial differential equations (PDEs) because they are flexible with respect to the geometry of the computational domain, they can…
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…
Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
Additive manufacturing technologies enable the production of complex and bioinspired shapes using magneto-responsive materials, which find diverse applications in soft robotics. Particularly, the development of composites with controlled…
Deterministic computational modeling of laser powder bed fusion (LPBF) process fails to capture irregularities and roughness of the scan track, unless expensive powder-scale analysis is used. In this work we developed a stochastic…
While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation…
Machine learning force fields (MLFFs) are gradually evolving towards enabling molecular dynamics simulations of molecules and materials with ab initio accuracy but at a small fraction of the computational cost. However, several challenges…
Computation of vorticity in conjunction with the strain rate tensor, plays an important role in fluid mechanics in vortical structure identification and in the modeling of various complex fluids. For the simulation of flows accompanied by…
In this paper we present a class of high order accurate cell-centered Arbitrary-Eulerian-Lagrangian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two-dimensional unstructured…
We present a unified framework for the construction of localized exponential integrators that bypasses the traditional trade-off between the accuracy of global spectral methods and the efficiency of sparse finite differences. By evaluating…