Asynchronous and corrected-asynchronous numerical solutions of parabolic PDES on MIMD multiprocessors

A major problem in achieving significant speed-up on parallel machines is the overhead involved with synchronizing the concurrent process. Removing the synchronization constraint has the potential of speeding up the computation. The authors present asynchronous (AS) and corrected-asynchronous (CA) finite difference schemes for the multi-dimensional heat equation. Although the discussion concentrates on the Euler scheme for the solution of the heat equation, it has the potential for being extended to other schemes and other parabolic partial differential equations (PDEs). These schemes are analyzed and implemented on the shared memory multi-user Sequent Balance machine. Numerical results for one and two dimensional problems are presented. It is shown experimentally that the synchronization penalty can be about 50 percent of run time: in most cases, the asynchronous scheme runs twice as fast as the parallel synchronous scheme. In general, the efficiency of the parallel schemes increases with processor load, with the time level, and with the problem dimension. The efficiency of the AS may reach 90 percent and over, but it provides accurate results only for steady-state values. The CA, on the other hand, is less efficient, but provides more accurate results for intermediate (non steady-state) values

DAG-based software frameworks for PDEs

pre-printThe task-based approach to software and parallelism is well-known and has been proposed as a potential candidate, named the silver model, for exas-cale software. This approach is not yet widely used in the large-scale multi-core parallel computing of complex systems of partial differential equations. After surveying task-based approaches we investigate how well the Uintah software and an extension named Wasatch fit in the task-based paradigm and how well they perform on large scale parallel computers. The conclusion is that these approaches show great promise for petascale but that considerable algorithmic challenges remain

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie