Related papers: A Domain Decomposition Approach for Local Mesh Ref…
Although learning-based image restoration methods have made significant progress, they still struggle with limited generalization to real-world scenarios due to the substantial domain gap caused by training on synthetic data. Existing…
This paper presents a three-scale computational strategy for the study of composite modeled at the mesoscale so that delamination can be reliably simulated. The solver is based on a LaTIn approach so that nonlinearities can be tackled at…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid the generation of body-fitted meshes and the use of graph…
This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
An adaptive mesh refinement and error estimation method for numerically solving optimal control problems is developed using Legendre-Gauss-Radau direct collocation. In regions of the solution where the desired accuracy tolerance has not…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
We present a three-dimensional (3D) common-refinement method for non-matching meshes between discrete non-overlapping subdomains of incompressible fluid and nonlinear hyperelastic structure. To begin, we first investigate the accuracy of…
This paper presents four novel domain decomposition algorithms integrated with nonlinear mapping techniques to address collocation-based solutions of eigenvalue problems involving sharp interfaces or steep gradients. The proposed methods…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…
Multiscale and inhomogeneous molecular systems are challenging topics in the field of molecular simulation. In particular, modeling biological systems in the context of multiscale simulations and exploring material properties are driving a…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a…