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Time to solution I n t e n s i t y R a t e O p e r a t i o n s p e r b y t e t r a n s f e r r e d D Abstract. Important computational physics problems are often large-scale in nature, and it is highly desirable to have robust and high performing computational frameworks that can quickly address these problems. However, it is no trivial task to determine whether a computational framework is performing efficiently or is scalable. The aim of this paper is to present various strategies for better understanding the performance of any parallel computational frameworks for solving PDEs. Important performance issues that negatively impact time-to-solution are discussed, and we propose a performance spectrum analysis that can enhance one's understanding of critical aforementioned performance issues. As proof of concept, we examine commonly used finite element simulation packages and software and apply the performance spectrum to quickly analyze the performance and scalability across various hardware platforms, software implementations, and numerical dis-cretizations. It is shown that the proposed performance spectrum is a versatile performance model that is not only extendable to more complex PDEs such as hydrostatic ice sheet flow equations, but also useful for understanding hardware performance in a massively parallel computing environment. Potential applications and future extensions of this work are also discussed.

FIDISOL is a program package for the solution of nonlinear systems of two-dimensional and three-dimensional elliptic and parabolic partial differential equations (PDEs) with nonlinear boundary conditions (BCs) on the boundaries of a rectangular domain. A finite difference method (FDM) with an arbitrary grid and arbitrary consistency order is used, these are either prescribed by the user or are self-adapted for a given relative tolerance. FIDISOL has been designed to be fully vectorizable on vector computers. In this paper we discuss several problems from the viewpoint of software development and user interface, for example, how to deliver the PDEs and BCs to FIDISOL and how to allow a flexible use by a suitable parameter list.

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