Related papers: Kranc: a Mathematica application to generate numer…
In this paper we present our recent work in developing a computer-algebra tool for systems of partial differential equations (PDEs), termed "Kranc". Our work is motivated by the problem of finding solutions of the Einstein equations through…
In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…
CARTAN is an easy-to-use symbolic, tensor component package based on the popular Mathematica program. CARTAN makes use of the powerful formalism of rigid frames, and can return results both in this frame and in the coordinate basis. CARTAN…
Work on different classification problems is described as: the classification of integrable vector evolution equations, NLS systems with two vector unknowns, systems with one scalar and one vector unknown, classification of integrable…
We consider the problem of low-rank approximation of massive dense non-negative tensor data, for example to discover latent patterns in video and imaging applications. As the size of data sets grows, single workstations are hitting…
In the field of scientific computing, one often finds several alternative software packages (with open or closed source code) for solving a specific problem. These packages sometimes even use alternative methodological approaches, e.g.,…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
Numerical simulations are becoming a more effective tool for conducting detailed investigations into the evolution of our universe. In this article, we show how the framework of numerical relativity can be used for studying cosmological…
The project, aimed at the theoretical support of experiments at modern and future accelerators -- TEVATRON, LHC, electron Linear Colliders (TESLA, NLC, CLIC) and muon factories, is presented. Within this project a four-level computer system…
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…
This paper reports the development of TOUCANS, a new Monte Carlo neutron transport code fully written using the Geant4 toolkit. It aims at modeling complex systems easily and rapidly, thanks to a simple key-value input file. While its main…
Designing optimisation algorithms that perform well in general requires experimentation on a range of diverse problems. Training neural networks is an optimisation task that has gained prominence with the recent successes of deep learning.…
A complete declarative description of the computational environment is often missing when researchers share their materials. Without such description, software obsolescence and missing system components can jeopardize computational…
The Portable Extensible Toolkit for Scientific Computation (PETSc) library provides scalable solvers for nonlinear time-dependent differential and algebraic equations and for numerical optimization via the Toolkit for Advanced Optimization…
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus…
A new algorithm is proposed to accelerate RANSAC model quality calculations. The method is based on partitioning the joint correspondence space, e.g., 2D-2D point correspondences, into a pair of regular grids. The grid cells are mapped by…
We present a C++ implementation of a fifth order semi-implicit Runge-Kutta algorithm for solving Ordinary Differential Equations. This algorithm can be used for studying many different problems and in particular it can be applied for…
Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…
Open-source simulation tools play a crucial role for neuromorphic application engineers and hardware architects to investigate performance bottlenecks and explore design optimizations before committing to silicon. Reconfigurable…
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no…