Related papers: Multiscale modeling for contact problem with high-…
In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation…
This paper presents a new fast multipole boundary element method (FM-BEM) for solving the acoustic transmission problems in 2D periodic media. We divide the periodic media into many fundamental blocks, and then construct the boundary…
The hyperelastic materials would contribute to the intricacies of rough surface contact, primarily due to the heightened nonlinearity caused by stress concentration. In our previous research, an incremental contact model tailored for…
In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
In this research, an online basis enrichment strategy for the constraint energy minimizing generalized multiscale finite element method in mixed formulation is proposed. The online approach is based on the technique of oversampling. One…
We improve the residual based stabilization technique for Signorini contact problems with Tresca friction in linear elasticity solved with $hp$-mixed BEM which has been recently analyzed by Banz et al.~in Numer.~Math.~135 (2017)…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
In this paper we propose simple multiscale basis functions with constraint energy minimization to solve elliptic problems with high contrast medium. Our methodology is based on the recently developed non-local multicontinuum method (NLMC).…
This article presents a higher-order spectral element method for the two-dimensional Stokes interface problem involving a piecewise constant viscosity coefficient. The proposed numerical formulation is based on least-squares formulation.…
We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the…
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then…
This article presents a new force model for performing quantitative simulations of dense granular materials. Interactions between multiple contacts (MC) on the same grain are explicitly taken into account. Our readily applicable method…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
In this paper, we propose an operator-inference-based reduction approach for contact problems, leveraging snapshots from simulations without active contact. Contact problems are solved using adjoint methods, by switching to the dual system,…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method…
Gradient schemes is a framework which enables the unified convergence analysis of many different methods -- such as finite elements (conforming, non-conforming and mixed) and finite volumes methods -- for $2^{\rm nd}$ order diffusion…
In this paper, we consider flow and transport problems in thin domains. The mathematical model considered in the paper is described by a system of equations for velocity, pressure, and concentration, where the flow is described by the…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…