Related papers: Benchmarking Domain-Specific Compiler Optimization…
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…
Domain-specific SoCs (DSSoCs) are attractive solutions for domains with stringent power/performance/area constraints; however, they suffer from two fundamental complexities. On the one hand, their many specialized hardware blocks result in…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
Optimizations in a traditional compiler are applied sequentially, with each optimization destructively modifying the program to produce a transformed program that is then passed to the next optimization. We present a new approach for…
With reference to a baseline parametrization, we explore highly efficient fractional factorial designs for inference on the main effects and, perhaps, some interactions. Our tools include approximate theory together with certain carefully…
Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework…
FEMSIM, a Fortran code, has been developed to simulate the fluctuation electron microscopy signal, the variance, V(k), from a model atomic structure. FEMSIM has been incorporated into a hybrid-reverse Monte Carlo code that combines an…
We investigate numerically efficient approximations of eigenspaces associated to symmetric and general matrices. The eigenspaces are factored into a fixed number of fundamental components that can be efficiently manipulated (we consider…
We introduce \texttt{featom}, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
In density-based topology optimization, design variables associated to the boundaries of the design domain require unique treatment to negate boundary effects arising from the filtering technique. An effective approach to deal with…
Foundation models have achieved tremendous success in different domains. However, their huge computation and storage complexity make these models difficult to fine-tune and also less applicable in practice. Recent study shows training in…
Fourier acceleration is a technique used in Hybrid Monte Carlo simulations to decrease the autocorrelation between subsequent field configurations in the generated ensemble. It has been shown, in the perturbative limit, to eliminate the…
We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…
Recent advancements in federated learning (FL) seek to increase client-level performance by fine-tuning client parameters on local data or personalizing architectures for the local task. Existing methods for such personalization either…
Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…