Related papers: Code generation for AMReX with applications to num…
We make available to the public 4 dark matter simulations that cover 4 CDM cosmological models and were run with the AP^3M code (Couchamn 1991). These simulations are described in Colin et al. (ApJ, 523, 32, 1999). There are about 20 epochs…
The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
Developers of Molecular Dynamics (MD) codes face significant challenges when adapting existing simulation packages to new hardware. In a continuously diversifying hardware landscape it becomes increasingly difficult for scientists to be…
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…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
As AI-based code generation becomes widespread, researchers are investigating the calibration of code LLMs - ensuring their confidence scores faithfully represent the true likelihood of code correctness. To do so, we investigate…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
We develop and modify the Adomian decomposition method (ADecM) to work for a new type of nonlinear matrix differential equations (MDE's) which arise in general relativity (GR) and possibly in other applications. The approach consists in…
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to…
Causal differencing has shown to be one of the promising and successful approaches towards excising curvature singularities from numerical simulations of black hole spacetimes. So far it has only been actively implemented in the ADM and…
LLM-based code generation tools are essential to help developers in the software development process. Existing tools often disconnect with the working context, i.e., the code repository, causing the generated code to be not similar to human…
This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows:…
This paper is dedicated to present an open-source program so-called \emph{AIMpy} built on Python language. \emph{AIMpy} is a solver for Schr\"{o}dinger-like differential equations using Asymptotic Iteration Method (AIM). To confirm the code…
In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…
Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of…
In this paper we discuss three symbolic approaches for the generation of a finite difference scheme of a partial differential equation (PDE). We prove, that for a linear PDE with constant coefficients these three approaches are equivalent…
Advancement in recent years in the field of experimental gravitation has allowed to test the equivalence principle in regimes that were previously unexplored, allowing for unprecedented verifications of general relativity and also enabling…
We present a new code, SCALAR, based on the high-resolution hydrodynamics and N-body code RAMSES, to solve the Schr\"odinger equation on adaptive refined meshes. The code is intended to be used to simulate axion or fuzzy dark matter models…
Automatic code generation for low-dimensional geometric algorithms is capable of producing efficient low-level software code through a high-level geometric domain specific language. Geometric Algebra (GA) is one of the most suitable…