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In this work, we revisit the marking decisions made in the standard adaptive finite element method (AFEM). Experience shows that a na\"{i}ve marking policy leads to inefficient use of computational resources for adaptive mesh refinement…
This paper presents an enhanced adaptive random Fourier features (ARFF) training algorithm for shallow neural networks, building upon the work introduced in "Adaptive Random Fourier Features with Metropolis Sampling", Kammonen et al.,…
Over the last decade block-structured adaptive mesh refinement (SAMR) has found increasing use in large, publicly available codes and frameworks. SAMR frameworks have evolved along different paths. Some have stayed focused on specific…
This paper presents a heterogeneous adaptive mesh refinement (AMR) framework for efficient simulation of moderately stiff reactive problems. This framework features an elaborate subcycling-in-time algorithm along with a specialized…
Structured Adaptive Mesh Refinement (SAMR) is a popular numerical technique to study processes with high spatial and temporal dynamic range. It reduces computational requirements by adapting the lattice on which the underlying differential…
We propose a mesh adaptation procedure for Cartesian quadtree meshes, to discretize scalar advection-diffusion-reaction problems. The adaptation process is driven by a recovery-based a posteriori estimator for the $L^2(\Omega)$-norm of the…
Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…
Bayesian curve fitting plays an important role in inverse problems, and is often addressed using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. However, this algorithm can be computationally inefficient without…
Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first…
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…
Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of complex physical phenomenon, as it allocates limited computational budget based on the need for higher or lower resolution, which varies over space and…
In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have…
Across a wide range of hardware scenarios, the computational efficiency and physical size of the arithmetic units significantly influence the speed and footprint of the overall hardware system. Nevertheless, the effectiveness of prior…
We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as…
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…
Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…
A fully threaded tree (FTT) for adaptive refinement of regular meshes is described. By using a tree threaded at all levels, tree traversals for finding nearest neighbors are avoided. All operations on a tree including tree modifications are…
Efficient topology optimization based on the adaptive auxiliary reduced model reanalysis (AARMR) is proposed to improve computational efficiency and scale. In this method, a projection auxiliary reduced model (PARM) is integrated into the…
Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…
Gravitational instabilities naturally give rise to multi-scale structure, which is difficult for traditional Eulerian hydrodynamic methods to accurately evolve. This can be circumvented by adaptively adding resolution (in the form of…