Related papers: Adaptive Radial Basis Function-generated Finite Di…
In this paper, we propose a novel unfitted finite element method for the simulation of multiple body contact. The computational mesh is generated independently of the geometry of the interacting solids, which can be arbitrarily complex. The…
We introduce a novel Bayesian phase estimation technique based on adaptive grid refinement method. This method automatically chooses the number particles needed for accurate phase estimation using grid refinement and cell merging strategies…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
An efficient method for finding all real roots of a univariate function in a given bounded domain is formulated. The proposed method uses adaptive mesh refinement to locate bracketing intervals based on bisection criterion for root finding.…
In this article, we present a three-dimensional anisotropic $hp$-mesh refinement strategy for ultraweak discontinuous Petrov--Galerkin (DPG) formulations with optimal test functions. The refinement strategy utilizes the built-in…
In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a…
The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete…
An improved finite difference method with compact correction term is proposed to solve the Poisson equations. The compact correction term is developed by a coupled high-order compact and low-order classical finite difference formulations.…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…
Gradient-based methods can efficiently optimize controllers by leveraging differentiable simulation and physical priors. However, contact-rich manipulation remains challenging because hybrid contact dynamics often produce discontinuous or…
We present a barrier method for treating frictional contact on interfaces embedded in finite elements. The barrier treatment has several attractive features, including: (i) it does not introduce any additional degrees of freedom or…
A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted,…
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…
The initial data for black hole collisions is constructed using a conformal-imaging approach and a new adaptive mesh refinement technique, a fully threaded tree (FTT). We developed a second-order accurate approach to the solution of the…
We develop the general form of the variational multiscale method in a discontinuous Galerkin framework. Our method is based on the decomposition of the true solution into discontinuous coarse-scale and discontinuous fine-scale parts. The…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
This article presents a general and novel approach to the automation of goal-oriented error control in the solution of nonlinear stationary finite element variational problems. The approach is based on automated linearization to obtain the…
We define a generalized finite element method for the discretization of elliptic partial differential equations in heterogeneous media. An adaptive local finite element basis (AL basis) on a coarse mesh which does not resolve the matrix of…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…