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A preasymptotic error analysis of the finite element method (FEM) and some continuous interior penalty finite element method (CIP-FEM) for Helmholtz equation in two and three dimensions is proposed. $H^1$- and $L^2$- error estimates with…
It is well known that to accelerate stencil codes on CPUs or GPUs and to exploit hardware caches and their lines optimizers must find spatial and temporal locality of array accesses to harvest data-reuse opportunities. On FPGAs there is the…
Mixture of experts (MoE) models achieve state-of-the-art results in language modeling but suffer from inefficient hardware utilization due to imbalanced token routing and communication overhead. While prior work has focused on optimizing…
Computational simulations using methods such as the finite element (FE) method rely on high-quality meshes for achieving accurate results. This study introduces a method for creating a high-quality hexahedral mesh using the Open Anatomy…
This paper presents an a priori error analysis of the hp-version of the boundary element method for the electric field integral equation on a piecewise plane (open or closed) Lipschitz surface. We use H(div)-conforming discretisations with…
The free energy principle (FEP), as an encompassing framework and a unified brain theory, has been widely applied to account for various problems in fields such as cognitive science, neuroscience, social interaction, and hermeneutics. As a…
In conventional spectral/finite element methods, the triangulation/quadrilateralization of the domain produces many interior edges which require additional DOF. What if we could directly use the original hull without going to…
The wide adoption of thermoplastic composites to reduce weight in structural parts requires reliable numerical methods to account for debonding between overmolded parts. Although cohesive elements are effective for debonding, the need for…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate mass matrix which is diagonal,…
We present a new software package, ``HexOpt,'' for improving the quality of all-hexahedral (all-hex) meshes by maximizing the minimum mixed scaled Jacobian-Jacobian energy functional, and projecting the surface points of the all-hex meshes…
Graphics processing units (GPUs) are continually evolving to cater to the computational demands of contemporary general-purpose workloads, particularly those driven by artificial intelligence (AI) utilizing deep learning techniques. A…
We present a spectral finite-element formulation of the optimized effective potential (OEP) method for atomic structure calculations in the random phase approximation (RPA). In particular, we develop a finite-element framework that employs…
This paper compares the performance of seven different element agglomeration algorithms on unstructured triangular/tetrahedral meshes when used as part of a geometric multigrid. Five of these algorithms come from the literature on AMGe…
This paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The…
The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…
We report the derivation and implementation of orbital optimization algorithms for the active space decomposition (ASD) model, which are extensions of complete active space self-consistent field (CASSCF) and its occupation-restricted…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…