Over the past two decades, some very efficient techniques for the numerical solution of partial differential equations have been developed. We are especially interested in adaptive local grid refinement on unstructured meshes, multigrid solvers and parallelization techniques. Up to now, these innovative techniques have been implemented mostly in university research codes and only very few commercial codes use them. There are two reasons for this. Firstly, the multigrid solution and adaptive refinement for many engineering applications are still a topic of active research and cannot be considered to be mature enough for routine application. Secondly, the implementation of all these techniques in a code with sufficient generality requires a lot of time and know-how in different fields. UG (abbreviation for Unstructured Grids) has been designed to overcome these problems. It provides very general tools for the generation and manipulation of unstructured meshes in two and three space dime...

The goal of this report is to survey state of the art and existing approaches for parallel programming on workstation clusters with special emphasis on object-oriented programming. First, workstation clusters as parallel computing platforms are characterized and fundamental concepts for parallel programming are discussed. Then, an overview of existing tools, systems, languages, and environments is given. The report concludes by identifying features of software systems suitable for parallel object-oriented programming on top of workstation clusters.

. We introduce the parallel grid manipulations needed in the Earth Science applications currently being implemented at the Data Assimilation Office (DAO) of the National Aeronautics and Space Administration (NASA). Due to real-time constraints the DAO software must run efficiently on parallel computers. Numerous grids, structured and unstructured are employed in the software. The DAO has implemented the PILGRIM library to support multiple grids and the various grid transformations between them, e.g., interpolations, rotations, prolongations and restrictions. It allows grids to be distributed over an array of processing elements (PEs) and manipulated with high parallel efficiency. The design of PILGRIM closely follows the DAO's requirements, but it can support other applications which employ certain types of grids. New grid definitions can be written to support still others. Results illustrate that PILGRIM can solve grid manipulation problems efficiently on parallel platforms such as th...

We present the special use of domain decomposition and operator splitting combined with asymptotic analytical qualitative results to obtain, on parallel computers, more efficient and accurate solvers [4] adapted to the nature of the solution of combustion fronts. Our applications in gas combustion, solid combustion as well as frontal polymerization are characterized by stiff fronts that propagate with nonlinear dynamics. The multiple scale phenomena under consideration lead to very intense computation and can be analysed formally by asymptotic methods [5, 6]. We focus our study here to combustion flame in liquid. Examples of liquid flames are given by reaction processes of frontal polymerization. Frontal polymerization is currently investigated to design new materials that cannot be produced by classical processes [15]. The interaction between a mechanism of convective instability similar to Rayleigh B'enard instability and a mechanism of thermal instability well known in solid combust...

igh quality libraries -- such as PETSc -- often use the OOP approach; yet scientists are more familiar with procedural programming. Finally, this project it is a good experience in building HPF "gasketware". How PETSc Might be used to Solve a Linear System call SLESCreate (MPICOMMWORLD, MySles, ierr) call SLESSetOperators (MySles, A, A, & DIFFERENTNONZEROPATTERN, ierr) call SLESSetFromOptions ( MySles, ierr) call SLESSolve ( MySles, b, x, iterations, ierr ) call SLESDestroy ( MySles, ierr) x is the approximate solution. It is a PETSc vector. A and b are the linear system. Usually A is given twice to SLESSetOperators, both as the input matrix and the preconditioner. To appreciate the flavor of PETSc, let's look at an example, as it would be coded in Fortran. This example is drawn from Shen and Davis, who experimented with PETSc. I put this up just to show you in which way the library is object oriented. 5<F

This office note discusses the design of PILGRIM, a library which will support the manipulations of grids in Earth Science software currently being designed and implemented at the Data Assimilation Office (DAO). It allows various grids to be distributed over an array of processing elements (PEs) and manipulated with high parallel efficiency. Unlike many parallel libraries, the developer takes some basic responsibility for laying out the data distribution. This adds to the simplicity of the implementation. Moreover, developers generally want some control of and understanding about the data's distribution. This is particularly true in the DAO's applications, e.g., GEOS DAS, in which data distributions are known in advance. PILGRIM has three distinct layers: low-level facilities to perform communication as well as basic linear algebra operations on distributed vectors, transformation kernels which work on distributed sparse matrices, and modules which define grid types and oper...