## Abstract

The modeling of physical phenomena in a variety of fields of scientific interest lead to a formulation in terms of partial differential equations. Especially when complex geometries as the domain of definition are involved, a direct and exact solution is not accessible, but numerical schemes are used to compute an approximate discrete solution. In this report, we focus on elliptic and parabolic types of equations that include spatial operators of second order. When discretizing such problems using commonly known discretization schemes such as finite element methods or finite volume methods, large systems of linear equations arise naturally. Their solution takes the largest amount of the overall computing time.

Original language | English (US) |
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Title of host publication | High Performance Computing in Science and Engineering '12 |

Subtitle of host publication | Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2012 |

Publisher | Springer-Verlag Berlin Heidelberg |

Pages | 435-449 |

Number of pages | 15 |

Volume | 9783642333743 |

ISBN (Electronic) | 9783642333743 |

ISBN (Print) | 3642333737, 9783642333736 |

DOIs | |

State | Published - Dec 1 2013 |

## ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)