Parallel object-oriented adaptive mesh refinement

In this paper we study adaptive mesh refinement (AMR) for elliptic and hyperbolic systems. We use the Asynchronous Fast Adaptive Composite Grid Method (AFACX), a parallel algorithm based upon the of Fast Adaptive Composite Grid Method (FAC) as a test case of an adaptive elliptic solver. For our hyperbolic system example we use TVD and ENO schemes for solving the Euler and MHD equations. We use the structured grid load balancer MLB as a tool for obtaining a load balanced distribution in a parallel environment. Parallel adaptive mesh refinement poses difficulties in expressing both the basic single grid solver, whether elliptic or hyperbolic, in a fashion that parallelizes seamlessly. It also requires that these basic solvers work together within the adaptive mesh refinement algorithm which uses the single grid solvers as one part of its adaptive solution process. We show that use of AMR++, an object-oriented library within the OVERTURE Framework, simplifies the development of AMR applications. Parallel support is provided and abstracted through the use of the P++ parallel array class

An object-oriented approach for parallel self adaptive mesh refinement on block structured grids

Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently

Parallel array classes and lightweight sharing mechanisms

ABSTRACT We discuss a set of parallel array classes, MetaMP, for distributed-memory architectures. The classes are implemented in C++ and interface to the PVM or Intel NX message-passing systems. An array class implements a partitioned array as a set of objects distributed across the nodes-a "collective" object. Object methods hide the low-level message-passing and implement meaningful array operations. These include transparent guard strips (or sharing regions) that support finite-difference stencils, reductions and multibroadcasts for support of pivoting and row operations, and interpolation/ contraction operations for support of multigrid algorithms. The concept of guard strips is generalized to an object implementation of lightweight sharing mechanisms for finite element method (FEM) and particle-in-cell (PIC) algorithms. The sharing is accomplished through the mechanism of weak memory coherence and can be efficiently implemented. The price of the efficient implementation is memory usage and the need to explicitly specify the coherence operations. An intriguing feature of this programming model is that it maps well to both distributed-memory and shared-memory architectures

Compositional C++: Compositional Parallel Programming

A compositional parallel program is a program constructed by composing component programs in parallel, where the composed program inherits properties of its components. In this paper, we describe a small extension of C++ called Compositional C++ or CC++ which is an object-oriented notation that supports compositional parallel programming. CC++ integrates different paradigms of parallel programming: data-parallel, task-parallel and object-parallel paradigms; imperative and declarative programming; shared memory and messagebased programs. CC++ is designed to be transportable across a range of MIMD architectures

An integrated runtime and compile-time approach for parallelizing structured and block structured applications

Scientific and engineering applications often involve structured meshes. These meshes may be nested (for multigrid codes) and/or irregularly coupled (called multiblock or irregularly coupled regular mesh problems). A combined runtime and compile-time approach for parallelizing these applications on distributed memory parallel machines in an efficient and machine-independent fashion was described. A runtime library which can be used to port these applications on distributed memory machines was designed and implemented. The library is currently implemented on several different systems. To further ease the task of application programmers, methods were developed for integrating this runtime library with compilers for HPK-like parallel programming languages. How this runtime library was integrated with the Fortran 90D compiler being developed at Syracuse University is discussed. Experimental results to demonstrate the efficacy of our approach are presented. A multiblock Navier-Stokes solver template and a multigrid code were experimented with. Our experimental results show that our primitives have low runtime communication overheads. Further, the compiler parallelized codes perform within 20 percent of the code parallelized by manually inserting calls to the runtime library

Doctor of Philosophy

dissertationIn the static analysis of functional programs, control- ow analysis (k-CFA) is a classic method of approximating program behavior as a infinite state automata. CFA2 and abstract garbage collection are two recent, yet orthogonal improvements, on k-CFA. CFA2 approximates program behavior as a pushdown system, using summarization for the stack. CFA2 can accurately approximate arbitrarily-deep recursive function calls, whereas k-CFA cannot. Abstract garbage collection removes unreachable values from the store/heap. If unreachable values are not removed from a static analysis, they can become reachable again, which pollutes the final analysis and makes it less precise. Unfortunately, as these two techniques were originally formulated, they are incompatible. CFA2's summarization technique for managing the stack obscures the stack such that abstract garbage collection is unable to examine the stack for reachable values. This dissertation presents introspective pushdown control-flow analysis, which manages the stack explicitly through stack changes (pushes and pops). Because this analysis is able to examine the stack by how it has changed, abstract garbage collection is able to examine the stack for reachable values. Thus, introspective pushdown control-flow analysis merges successfully the benefits of CFA2 and abstract garbage collection to create a more precise static analysis. Additionally, the high-performance computing community has viewed functional programming techniques and tools as lacking the efficiency necessary for their applications. Nebo is a declarative domain-specific language embedded in C++ for discretizing partial differential equations for transport phenomena. For efficient execution, Nebo exploits a version of expression templates, based on the C++ template system, which is a type-less, completely-pure, Turing-complete functional language with burdensome syntax. Nebo's declarative syntax supports functional tools, such as point-wise lifting of complex expressions and functional composition of stencil operators. Nebo's primary abstraction is mathematical assignment, which separates what a calculation does from how that calculation is executed. Currently Nebo supports single-core execution, multicore (thread-based) parallel execution, and GPU execution. With single-core execution, Nebo performs on par with the loops and code that it replaces in Wasatch, a pre-existing high-performance simulation project. With multicore (thread-based) execution, Nebo can linearly scale (with roughly 90% efficiency) up to 6 processors, compared to its single-core execution. Moreover, Nebo's GPU execution can be up to 37x faster than its single-core execution. Finally, Wasatch (the pre-existing high-performance simulation project which uses Nebo) can scale up to 262K cores

Ein Modell zur effizienten Parallelisierung von Algorithmen auf komplexen, dynamischen Datenstrukturen

Moderne berechnungsintensive Algorithmen, beispielsweise adaptive numerische Lösungsverfahren für partielle Differentialgleichungen, arbeiten oftmals auf komplexen, dynamischen Datenstrukturen. Die Implementierung solcher Algorithmen auf Parallelrechnern mit verteiltem Speicher mittels Datenpartitionierung wirft zahlreiche Probleme auf (z.B. Lastverteilung). Im Rahmen der vorliegenden Arbeit wurde das neue parallele Programmiermodell Dynamic Distributed Data (DDD) entwickelt, durch das die Parallelisierungsarbeit vom Design der verteilten Datenstrukturen bis hin zur Erstellung des portablen, parallelen und effizienten Programmcodes unterstützt wird. Dem DDD-Konzept liegt ein graphbasiertes formales Modell zugrunde. Dabei wird die Datenstruktur des jeweiligen Programms (z.B. unstrukturierte Gitter) formal auf einen verteilten Graphen abgebildet, der aus mehreren lokalen Graphen besteht. Das formale Modell dient als Spezifikation des Programmiermodells und gleichzeitig zur Definition der wichtigen in dieser Arbeit verwendeten Begriffe. Der Systemarchitektur von DDD-basierten Anwendungen liegt ein Schichtenmodell zugrunde, den Kern stellt dabei die DDD-Programmbibliothek dar. Diese bietet Funktionen zur dynamischen Definition verteilter Datentypen und zur Verwaltung lokaler Objekte. In den Überlappungsbereichen der lokalen Graphen stehen abstrakte Kommunikationsfunktionen in Form von sog. Interfaces zur Verfügung. Die wesentliche Neuerung gegenüber nahezu allen bestehenden Arbeiten ist jedoch die Möglichkeit zur dynamischen Veränderung des verteilten Graphen; dies ermöglicht es beispielsweise, dynamische Lastverteilung oder Gittergenerierungsverfahren einfach und effizient zu implementieren. Damit können beliebig komplexe Datentopologien dynamisch erzeugt, migriert und wieder entfernt werden

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth