Mathematical Software
Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system's behaviour changes over time. A key problem in time series modelling is \emph{inference}; determining properties of…
The solution of (generalized) eigenvalue problems for symmetric or Hermitian matrices is a common subtask of many numerical calculations in electronic structure theory or materials science. Solving the eigenvalue problem can easily amount…
We address the problem of optimizing mixed sparse and dense tensor algebra in a compiler. We show that standard loop transformations, such as strip-mining, tiling, collapsing, parallelization and vectorization, can be applied to irregular…
The translation of linear algebra computations into efficient sequences of library calls is a non-trivial task that requires expertise in both linear algebra and high-performance computing. Almost all high-level languages and libraries for…
Multi-dimensional discrete Fourier transforms (DFT) are typically decomposed into multiple 1D transforms. Hence, parallel implementations of any multi-dimensional DFT focus on parallelizing within or across the 1D DFT. Existing DFT packages…
We present the Alsvinn simulator, a fast multi general purpose graphical processing unit (GPGPU) finite volume solver for hyperbolic conservation laws in multiple space dimensions. Alsvinn has native support for uncertainty quantifications,…
Driven by the insatiable needs to process ever larger amount of data with more complex models, modern computer processors and accelerators are beginning to offer half precision floating point arithmetic support, and extremely optimized…
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…
CheasePy is code written in Python to run the CHEASE (Cubic Hermite Element Axisymmetric Static Equilibrium) code, which solves the Grad-Shafranov equation for toroidal MHD equilibria using pressure and current profiles and fixed plasma…
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to a…
This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory…
On common processors, integer multiplication is many times faster than integer division. Dividing a numerator n by a divisor d is mathematically equivalent to multiplication by the inverse of the divisor (n / d = n x 1/d). If the divisor is…
A new method to construct task graphs for \mcH-matrix arithmetic is introduced, which uses the information associated with all tasks of the standard recursive \mcH-matrix algorithms, e.g., the block index set of the matrix blocks involved…
For the parallel-in-time integration method Parareal, pipelining can be used to hide some of the cost of the serial correction step and improve its efficiency. The paper introduces a basic OpenMP implementation of pipelined Parareal and…
In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…
We present our effort to extend and complement the core modules of the Distributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key…
Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely…
Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards…