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An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…

We present a simple and efficient MATLAB implementation of the local refinement for polygonal meshes. The purpose of this implementation is primarily educational, especially on the teaching of adaptive virtual element methods.

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…

Adaptive mesh refinement (AMR) is a classical technique about local refinement in space where needed, thus effectively reducing computational costs for HPC-based physics simulations. Although AMR has been used for many years, little…

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…

The present paper describes a parallel unstructured-mesh Plasma simulation code based on Finite Volume method. The code dynamically refines and coarses mesh for accurate resolution of the different features regarding the electron density.…

We review a scalable two- and three-dimensional computer code for low-temperature plasma simulations in multi-material complex geometries. Our approach is based on embedded boundary (EB) finite volume discretizations of the minimal…

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with…

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

Finite element discretizations of problems in computational physics often rely on adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. However, these spatial refinement strategies…

Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…

In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…

Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement…

In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…

The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms that are nodes for a finite element triangulation. In regions of the…

Several applications in astrophysics require adequately resolving many physical and temporal scales which vary over several orders of magnitude. Adaptive mesh refinement techniques address this problem effectively but often result in…

Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…

Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…