pdelib Algorithms and software

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`pdelib` -- Algorithms and software components for the numerical solution of partial differential equations

J. Fuhrmann , K. Gärtner , H. Langmach

Description:

The purpose of this project is the maintenance and further development of pdelib , a toolbox of software components for the numerical solution of partial differential equations. During the last year, efforts have been undertaken in order to develop a prototype of the new pdelib2 kernel which is aimed at higher efficiency especially in the context of three-dimensional simulations while maintaining the modular structure of the existing version.

The present state is characterized by

Shared memory parallelization of grid access and linear algebra. A parallelization layer has been developed which, depending on the available compilers, allows to work either with the pthreads library or OpenMP compiler directives.
Equally efficient access of node-, edge-, facet- and cell-based degrees of freedom. This is facilitated by a mesh data structure based on adjacency matrices stored in index lists. On top of this, higher-order finite element functionality shall be implemented.
Vectorizable element callback functions. In difference to the existing pdelib implementation, the atomic mesh item accessed by the user is a list of elements rather than a single element. In this way, superscalar optimizations and efficient cache re-use are organized. Furthermore, a modularization based on an element list level is connected with far less function call overhead.
Efficient search functions on simplicial meshes;
User input in the Lua language. The whole Lua user interface is restructured. The user can access mathematical objects like vectors, block vectors, and matrices in a mathematically motivated manner, similar to, e.g., matlab.
Integration of TetGen (3D) and triangle (2D) boundary-conforming Delaunay mesh generation tools. A user of pdelib2 will be able to describe the geometry in the Lua language. The corresponding data are directly fed to the mesh generators using the triangulateio resp. tetgenio data structures provided by them.
Integration of COG;
Support of complex numbers.