A GPU-enabled implicit Finite Volume solver for the ideal two-fluid plasma model on unstructured grids

This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been implemented within the open source COOLFluiD platform, is implicit, second-order in time and space, relying upon a Finite Volume method for the spatial discretization and a three-point backward Euler for the time integration. In particular, the convective fluxes are computed by a multi-fluid version of the AUSM+up scheme for the plasma equations, in combination with a modified Rusanov scheme with tunable dissipation for the Maxwell equations. Source terms are integrated with a one-point rule, using the cell-centered value. Some critical aspects of the porting to GPU's are discussed, as well as the performance of two open source linear system solvers (i.e. PETSc, PARALUTION). The code design allows for computing both flux and source terms on the GPU along with their Jacobian, giving a noticeable decrease in the computational time in comparison with the original CPU-based solver. The code has been tested in a wide range of mesh sizes and in three different systems, each one with a different GPU. The increased performance (up to 14x) is demonstrated in two representative 2D benchmarks: propagation of circularly polarized waves and the more challenging Geospace Environmental Modeling (GEM) magnetic reconnection challenge.Comment: 22 pages, 7 figure

Odeint - Solving ordinary differential equations in C++

Many physical, biological or chemical systems are modeled by ordinary differential equations (ODEs) and finding their solution is an every-day-task for many scientists. Here, we introduce a new C++ library dedicated to find numerical solutions of initial value problems of ODEs: odeint (www.odeint.com). odeint is implemented in a highly generic way and provides extensive interoperability at top performance. For example, due to it's modular design it can be easily parallized with OpenMP and even runs on CUDA GPUs. Despite that, it provides a convenient interface that allows for a simple and easy usage.Comment: 4 pages, 1 figur

QuTiP: An open-source Python framework for the dynamics of open quantum systems

We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte-Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well-suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.Comment: 16 pages, 12 figure

Numerical simulation of the stress-strain state of the dental system

We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk of overloading the supporting elements. Such risk can be avoided by the proper load distribution and prediction of stresses that occur during the use of dentures. We developed the mathematical model of the periodontal complex and its software implementation. This model is based on linear elasticity theory and allows to calculate the stress and strain fields in periodontal ligament and jawbone. The input parameters for the developed model can be divided into two groups. The first group of parameters describes the mechanical properties of periodontal ligament, teeth and jawbone (for example, elasticity of periodontal ligament etc.). The second group characterized the geometric properties of objects: the size of the teeth, their spatial coordinates, the size of periodontal ligament etc. The mechanical properties are the same for almost all, but the input of geometrical data is complicated because of their individual characteristics. In this connection, we develop algorithms and software for processing of images obtained by computed tomography (CT) scanner and for constructing individual digital model of the tooth-periodontal ligament-jawbone system of the patient. Integration of models and algorithms described allows to carry out biomechanical analysis on three-dimensional digital model and to select prosthesis design.Comment: 19 pages, 9 figure

ParMooN - a modernized program package based on mapped finite elements

{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of {\sc ParMooN}. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library {\sc PETSc}. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.Comment: partly supported by European Union (EU), Horizon 2020, Marie Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant number 67571