Related papers: A study of vectorization for matrix-free finite el…
This paper presents efficient data structures for the implementation of matrix-free finite element methods on block-structured, hybrid tetrahedral grids. It provides a complete categorization of all geometric sub-objects that emerge from…
We present an efficient algorithmic framework for constructing multi-level hp-bases that uses a data-oriented approach that easily extends to any number of dimensions and provides a natural framework for performance-optimized…
Kernel matrix-vector multiplication (KMVM) is a foundational operation in machine learning and scientific computing. However, as KMVM tends to scale quadratically in both memory and time, applications are often limited by these…
We examine the Xeon Phi, which is based on Intel's Many Integrated Cores architecture, for its suitability to run the FDK algorithm--the most commonly used algorithm to perform the 3D image reconstruction in cone-beam computed tomography.…
In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE)…
We present a novel, quadrature-based finite element integration method for low-order elements on GPUs, using a pattern we call \textit{thread transposition} to avoid reductions while vectorizing aggressively. On the NVIDIA GTX580, which has…
The modeling of electric machines and power transformers typically involves systems of nonlinear magnetostatics or -quasistatics, and their efficient and accurate simulation is required for the reliable design, control, and optimization of…
Traditional solution approaches for problems in quantum mechanics scale as $\mathcal O(M^3)$, where $M$ is the number of electrons. Various methods have been proposed to address this issue and obtain linear scaling $\mathcal O(M)$. One…
Rahman and Valdman (2013) introduced a new vectorized way to assemble finite element matrices. We utilize underlying vectorization concepts and extend MATLAB codes to implementation of Bogner-Fox-Schmit C1 rectangular elements in 2D. Our…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
Full-wave 3D electromagnetic simulations of complex planar devices, multilayer interconnects, and chip packages are presented for wide-band frequency-domain analysis using the finite difference integration technique developed in the PETSc…
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…
The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and…
FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting…
The capacity to predict and control bioprocesses is perhaps one of the most important objectives of biotechnology. Computational simulation is an established methodology for the design and optimization of bioprocesses, where the finite…
The layer-upon-layer approach in additive manufacturing, open or closed cells in polymeric or metallic foams involve an intrinsic microstructure tailored to the underlying applications. Homogenization of such architectured materials creates…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
Nonlinear energy functionals appearing in the calculus of variations can be discretized by the finite element (FE) method and formulated as a sum of energy contributions from local elements. A fast evaluation of energy functionals…
In this paper, we propose a fast algorithm for element selection, a multiplication-free form of dimension reduction that produces a dimension-reduced vector by simply selecting a subset of elements from the input. Dimension reduction is a…
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems…