Topic Area: Solutions
Dhavide Aruliah, Associate Professor, Faculty of Science, University of Ontario Institute of Technology (UOIT)
A Parallel Adaptive Method for Pseudo-Arclength Continuation
Pseudo-arclength continuation is a well-established method for con- structing a numerical curve comprising solutions of a system of nonlinear equations. The usual predictor-corrector scheme involves a prediction of a prescribed step-length along a tangent direction followed by correction steps (typically using Newton’s method) in a hyperplane containing the prediction point. In many complicated high-dimensional systems, the cor- rections steps can be extremely costly to compute; as a result, the step- length of the original prediction step must be chosen carefully to avoid prohibitively many failed steps and corresponding wasted CPU cycles. We present a parallel method for adapting the step-length of pseudo- arclength continuation. Our method employs several predictor-corrector sequences run concurrently on distinct processors with differing step- lengths. Our parallel framework permits intermediate results of uncon- verged correction sequences to seed new predictor-corrector sequences with various step-lengths; the goal is to amortise the cost of corrector steps to make further progress along the underlying numerical curve. We describe the essence of the parallel algorithm and provide evidence from numerical experiments to support its efficacy. Results from numeri- cal experiments suggest that a three-fold speed-up is attainable when the continuation curve sought has great topological complexity and the cor- rector steps require significant processor time. Our implementation can be used without extensive experience with High-Performance Computing; users need only supply a routine for computing the corrector steps.
Raymond Spiteri, Professor, Department of Computer Science, University of Saskatchewan
The Significance of Order in the Numerical Simulation of the BiDomain Equation in Parallel
The propagation of electrical activity in the heart can be modelled by the bidomain equations. However to obtain clinically useful data from the bidomain equations, they must be solved with many millions of unknowns. Naturally, to obtain such data in real time is the ultimate goal, but at present we are still an order of magnitude or two away from being able to do so. The spectral/hp element method can be considered to be a high-order extension of the traditional “finite” or “spectral” element methods, where convergence is not only possible through reducing the mesh size h but also through increasing the local polynomial order p of the basis functions used to expand the solution. We are interested in evaluating the effectiveness of a high-order method in serial against that of a low-order method in parallel. We find that high-order methods in serial can outperform low-order methods in parallel. These findings suggest software developers for the bidomain equations should not forego the implementation of high-order methods in their efforts to parallelize their solvers..
Topic Area: GPU
Varvara Roubtsova, Institut de recherche d’Hydro-Quebec
Parallel Algorithm for Fractal Scaling of Soil Particle-Size Distributions
This study is a part of an extensive program which includes 2-D and 3-D simulations aimed at gaining better understanding of erosion phenomena in soils made up of irregularly shaped particles under hydrodynamic flow. To simulate the soil in 2-D we use a fractal scaling of the soil particle-size distribution. The sequential algorithm of this model is based on an 11 levels deep nested loop in which the inner limits are dependent on the previous iteration. In this article we describe the parallel algorithm for this type of problem which avoids the dependent recursion by using a flattened generator. For portability, we chose the OpenCL (Open Computing Language) framework, which offers an abstract view of the parallel architecture used. To present the results we use the 3-D Alyoscopy. This technology allows multiple observers to interact with a simulation, and permits more complex systems to be viewed. Finally we present the results of the hydrodynamic flow through four different soil samples generated by the fractal model to validate the algorithm.
General: Faculty, staff, students
Thursday, May 3rd
2:20 – 3:30 p.m.
Canfor Policy Room
Roman Baranowski, WestGrid Site Lead, University of British Columbia