相关论文: A matched alternating direction implicit (ADI) met…
The direct-forcing immersed boundary method (DF-IBM) algorithm previously developed by the authors is extended by coupling the Navier-Stokes equations with the Newton-Euler equations for rigid body dynamics within the DF-IBM framework. This…
This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution…
This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is…
The seven-equation model is a compressible multiphase formulation that allows for phasic velocity and pressure disequilibrium. These equations are solved using a diffused interface method that models resolved multiphase flows. Novel…
We present a novel multiscale numerical approach that combines parallel-in-time computation with hybrid domain adaptation for linear collisional kinetic equations in the diffusive regime. The method addresses the computational challenges of…
This paper describes a novel partitioned algorithm for fluid-structure interaction (FSI) problems that couples the motion of rigid bodies and incompressible flow. This is the first partitioned algorithm that remains stable and second-order…
Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail…
Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…
The study proposes a data-driven model which combines the Dynamic Mode Decomposition with multi-linear interpolation to predict the thermal fields of nanofluid flows at unseen Reynolds numbers (Re) and particle volume concentrations…
Transform Invariant Low-rank Textures (TILT) is a novel and powerful tool that can effectively rectify a rich class of low-rank textures in 3D scenes from 2D images despite significant deformation and corruption. The existing algorithm for…
We propose a second-order temporally implicit, fourth-order-accurate spatial discretization scheme for the strongly anisotropic heat transport equation characteristic of hot, fusion-grade plasmas. Following [Du Toit et al., Comp. Phys.…
We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several…
We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…
A second-order-accurate finite volume method, hybridized by blending an extended double-flux algorithm and a traditionally conservative scheme, is developed. In this scheme, hybrid convective fluxes as well as hybrid interpolation…
We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
We develop a universally applicable embedded boundary finite difference method, which results in a symmetric positive definite linear system and does not suffer from small cell stiffness. Our discretization is efficient for the wave, heat…
Atmospheric powered descent guidance can be solved by successive convexification; however, its onboard application is impeded by the sharp increase in computation caused by nonlinear aerodynamic forces. The problem has to be converted into…
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…