Related papers: Hybridized Isogeometric Method for Elliptic Proble…
This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformulating the contact problem as a nonlinear variational…
We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…
Elliptic partial differential equations are important both from application and analysis points of views. In this paper we apply the Closest Point Method to solving elliptic equations on general curved surfaces. Based on the closest point…
This paper addresses optimal design problems governed by multi-state stationary diffusion equations, aiming at the simultaneous optimization of the domain shape and the distribution of two isotropic materials in prescribed proportions.…
Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
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.…
Trimming is a common operation in CAD, and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming the geometric description of the patch remains…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. The construction is applied in two settings. First, we show…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.
Elliptic homogenization is used to determine coarse-grained properties of materials with features on small scales for heat transfer and elasticity. When microstructural features of a material have rapid, periodic fluctuations, the solution…
In this paper, we propose a hybrid collocation method based on finite difference and Haar wavelets to solve nonlocal hyperbolic partial differential equations. Developing an efficient and accurate numerical method to solve such problem is a…
We present an efficient method for the computation of homogenized coefficients of divergence-form operators with random coefficients. The approach is based on a multiscale representation of the homogenized coefficients. We then implement…