Abstract:This paper presents the design, development and application of a computational infrastructure to support the implementation of parallel adaptive algorithms for the solution of sets of partial differential equations. The infrastructure is separated into multiple layers of abstraction. This paper is primarily concerned with the two lowest layersof this infrastructure: a layer which defines and implements dynamic distributed arrays (DDA), and a layer in which several dynamic data and programming abstractions are implemented in terms of the DDAs. The currently implemented abstractions are those needed for formulation of hierarchical adaptive finite difference methods, hp-adaptive finite element methods, and fast multipole method for solution of linear systems. Implementation of sample applications based on each of these methods are described and implementation issues and performance measurements are presented.

Over the past twenty y ears, dense linear algebra libraries have gone through three generations of public domain general purpose packages. In the seventies, the rst generation of packages were EISPACK and LINPACK, which implemented a broad spectrum of algorithms for solving dense linear eigenproblems and dense linear systems. In the late eighties, the second generation package called LAPACK was developed. This package attains high performance in a portable fashion while also improving upon the functionality and robustness of LINPACK and EISPACK. Finally, since the early nineties, a third generation package which ports LAPACK to distributed memory networks of computers has been underway a s p a r t o f t h e ScaLAPACK project.PLAPACKis a maturing fourth generation package which uses a more application-centric view of vector and matrix distribution, Physically Based Matrix Distribut ion. It also uses an \MPI-like" programming interface that hides distribution and indexing details in opaque objects, provides a natural layering in the library, a n d p r o vides a straight-forward application interface. In this paper, we give a n o verview of the design of PLAPACK.i