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An extension of the framework of the Finite Integration Technique (FIT) including dynamic and adaptive mesh refinement is presented. After recalling the standard formulation of the FIT, the proposed mesh adaptation procedure is described.…
Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent generating complex 3D interface-fitted meshes. However, many…
This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO…
This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
We present an algorithm for $hp$-adaptive collocation-based mesh-free numerical analysis of partial differential equations. Our solution procedure follows a well-established iterative solve-estimate-mark-refine paradigm. The solve phase…
We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, we are interested in an accurate computation of some…
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…
We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types 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…
This work is related to PHG (Parallel Hierarchical Grid). PHG is a toolbox for developing parallel adaptive finite element programs, which is under active development at the State Key Laboratory of Scientific and Engineering Computing. The…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…
Benchmarking is essential for testing new numerical analysis codes. Their solution is crucial both for testing the partial differential equation solvers and both for the optimization methods. Especially, nature-inspired optimization…
Mixed integer linear programs are commonly solved by Branch and Bound algorithms. A key factor of the efficiency of the most successful commercial solvers is their fine-tuned heuristics. In this paper, we leverage patterns in real-world…
The a posteriori error analysis of the classical Argyris finite element methods dates back to 1996, while the optimal convergence rates of associated adaptive finite element schemes are established only very recently in 2021. It took a long…
When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…