Related papers: fmmgen: Automatic Code Generation of Operators for…
A compiler approach for generating low-level computer code from high-level input for discontinuous Galerkin finite element forms is presented. The input language mirrors conventional mathematical notation, and the compiler generates…
We show a new algorithm and its implementation for multiplying bit-polynomials of large degrees. The algorithm is based on evaluating polynomials at a specific set comprising a natural set for evaluation with additive FFT and a high order…
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…
The construction of quantum computers is based on the synthesis of low-cost quantum circuits. The quantum circuit of any Boolean function expressed in a Positive Polarity Reed-Muller $PPRM$ expansion can be synthesized using…
Deep learning models typically use single-precision (FP32) floating point data types for representing activations and weights, but a slew of recent research work has shown that computations with reduced-precision data types (FP16, 16-bit…
We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…
We present the Flowgen tool, which generates flowcharts from annotated C++ source code. The tool generates a set of interconnected high-level UML activity diagrams, one for each function or method in the C++ sources. It provides a simple…
In boundary element methods (BEM) in $\mathbb{R}^3$, matrix elements and right hand sides are typically computed via analytical or numerical quadrature of the layer potential multiplied by some function over line, triangle and tetrahedral…
The brain is probably the most complex organ in the human body. To understand processes such as learning or healing after brain lesions, we need suitable tools for brain simulations. The Model of Structural Plasticity offers a solution to…
Among the algorithms that are likely to play a major role in future exascale computing, the fast multipole method (FMM) appears as a rising star. Our previous recent work showed scaling of an FMM on GPU clusters, with problem sizes in the…
The \emph{Fast Gaussian Transform} (FGT) enables subquadratic-time multiplication of an $n\times n$ Gaussian kernel matrix $\mathsf{K}_{i,j}= \exp ( - \| x_i - x_j \|_2^2 ) $ with an arbitrary vector $h \in \mathbb{R}^n$, where $x_1,\dots,…
Large Language Models (LLMs) have sparked significant interest in their generative capabilities, leading to the development of various commercial applications. The high cost of using the models drives application builders to maximize the…
Fast multipole methods have O(N) complexity, are compute bound, and require very little synchronization, which makes them a favorable algorithm on next-generation supercomputers. Their most common application is to accelerate N-body…
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
Magneto-static finite element (FE) simulations make numerical optimization of electrical machines very time-consuming and computationally intensive during the design stage. In this paper, we present the application of a hybrid data-and…
Abstract Machine learning models, trained on data from ab initio quantum simulations, are yielding molecular dynamics potentials with unprecedented accuracy. One limiting factor is the quantity of available training data, which can be…
This paper presents an octree construction method, called Cornerstone, that facilitates global domain decomposition and interactions between particles in mesh-free numerical simulations. Our method is based on algorithms developed for 3D…
Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes. This calls for continuous efforts in code development, which is necessitated…
Automated code generation using large language models (LLMs) has gained attention due to its efficiency and adaptability. However, real-world coding tasks or benchmarks like HumanEval and StudentEval often lack dedicated training datasets,…
A new implementation of many-body calculations is of paramount importance in the field of computational physics. In this study, we leverage the capabilities of Field Programmable Gate Arrays (FPGAs) for conducting quantum many-body…