Jianping Zhu

An efficient high-order algorithm for solving systems of 3-D reaction-diffusion equations

We discuss an efficient higher order finite difference algorithm for solving systems of 3-D reaction-diffusion equations with nonlinear reaction terms. The algorithm is fourth-order accurate in both the temporal and spatial dimensions. It requires only a regular seven-point difference stencil similar to that used in the standard second-order algorithms, such as the Crank-Nicolson algorithm. Numerical examples are presented to demonstrate the efficiency and accuracy of the new algorithm.

Performance considerations of shared virtual memory machines

Generalized speedup is defined as parallel speed over sequential speed. In this paper the generalized speedup and its relation with other existing performance metrics, such as traditional speedup, efficiency, scalability, etc., are carefully studied. In terms of the introduced asymptotic speed, we show that the difference between the generalized speedup and the traditional speedup lies in the definition of the efficiency of uniprocessor processing, which is a very important issue in shared virtual memory machines. A scientific application has been implemented on a KSR-1 parallel computer. Experimental and theoretical results show that the generalized speedup is distinct from the traditional speedup and provides a more reasonable measurement. In the study of different speedups, an interesting relation between fixed-time and memory-bounded speedup is revealed. Various causes of superlinear speedup are also presented.

Performance prediction. A case study using a scalable shared-virtual memory machine

A simple formula shows the relationship between scalability, single-processor computing power, and degradation of parallelism. Starting with this formula, the authors investigate the prediction and application of scalability.

Message-passing parallel adaptive quantum trajectory method

Time-dependent wavepackets are widely used to model various phenomena in physics. One approach in simulating the wavepacket dynamics is the quantum trajectory method (QTM). Based on the hydrodynamic formulation of quantum mechanics, the QTM represents the wavepacket by an unstructured set of pseudoparticles whose trajectories are coupled by the quantum potential. The governing equations for the pseudoparticle trajectories are solved using a computationally-intensive moving weighted least squares (MWLS) algorithm, and the trajectories can be computed in parallel. This work contributes a strategy for improving the performance of wavepacket simulations using the QTM on message-passing systems. Specifically, adaptivity is incorporated into the MWLS algorithm, and loop scheduling is employed to dynamically load balance the parallel computation of the trajectories. The adaptive MWLS algorithm reduces the amount of computations without sacrificing accuracy, while adaptive loop scheduling addresses the load imbalance introduced by the algorithm and the runtime system. Results of experiments on a Linux cluster are presented to confirm that the adaptive MWLS reduces the trajectory computation time by up to 24%, and adaptive loop scheduling achieves parallel effieciencies of up to 90% when simulating a free particle.

Shared virtual memory and generalized speedup

Generalized speedup is defined as parallel speed over sequential speed. In this paper the generalized speedup and its relation with other existing performance metrics, such as traditional speedup, efficiency, scalability, etc., are carefully studied. In terms of the introduced asymptotic speed, it is shown that the difference between the generalized speedup and the traditional speedup lies in the definition of the efficiency of uniprocessor processing, which is a very important issue in shared virtual memory machines. A scientific application has been implemented on a KSR-1 parallel computer. Experimental and theoretical results show that the generalized speedup is distinct from the traditional speedup and provides a more reasonable measurement. In the study of different speedups, various causes of superlinear speedup are also presented.<<ETX>>

An Efficient Parallel Algorithm with Application to Computational Fluid Dynamics

Abstract When solving time-dependent partial differential equations on parallel computers using the nonoverlapping domain decomposition method, one often needs numerical boundary conditions on the boundaries between subdomains. These numerical boundary conditions can significantly affect the stability and accuracy of the final algorithm. In this paper, a stability and accuracy analysis of the existing methods for generating numerical boundary conditions will be presented, and a new approach based on explicit predictors and implicit correctors will be used to solve convection-diffusion equations on parallel computers, with application to aerospace engineering for the solution of Euler equations in computational fluid dynamics simulations. Both theoretical analyses and numerical results demonstrate significant improvement in stability and accuracy by using the new approach.

Parallel adaptive quantum trajectory method for wavepacket simulations

Time-dependent wavepackets are widely used to model various phenomena in physics. One approach in simulating the wavepacket dynamics is the quantum trajectory method (QTM). Based on the hydrodynamic formulation of quantum mechanics, the QTM represents the wavepacket by an unstructured set of pseudoparticles whose trajectories are coupled by the quantum potential. The governing equations for the pseudoparticle trajectories are solved using a computationally intensive moving weighted least squares (MWLS) algorithm, and the trajectories can be computed in parallel. This paper contributes a strategy for improving the performance of wavepacket simulations using the QTM. Specifically, adaptivity is incorporated into the MWLS algorithm, and loop scheduling techniques are employed to dynamically load balance the parallel computation of the trajectories. The adaptive MWLS algorithm reduces the amount of computations without sacrificing accuracy, while adaptive loop scheduling addresses the load imbalance introduced by the algorithm and the runtime system. Results of experiments on a Linux cluster are presented to confirm that the adaptive MWLS reduces the trajectory computation time by up to 24%, and adaptive loop scheduling achieves parallel efficiencies of up to 85% when simulating a free particle.

A web-based simulation system for transport and retention of dissolved contaminants in soil

Abstract The movement of contaminants through the soil matrix is primarily a liquid phase process in which the chemical partitions between sorbed and dissolved phases. These phenomena have been modeled extensively and several computer models were developed. The use of those computer programs requires installation of the software in the users machine. Usually, post-processing of the numerical output provided by the software is required. In this paper, a web-based simulation environment for retention and transport of dissolved organic and inorganic compounds in soils is presented. The system was developed using Java and is based on the Multi-reaction Transport Model of heavy metals in soil. The mathematical and numerical formulation of the model is briefly sketched. The core computing components of the simulation environment were written in C or fortran for their computational efficiency. The emerging Java Native Interface (JNI) technique and the Swing interface were used to design a user-friendly simulator. Java security problems (due to the use of applets calling native libraries) are discussed and a solution to avoid security restrictions is provided. The simulation system provides interactive user control and real time visualization through standard web browsers. The Java-based simulation code was used to analyze a hypothetical soil contamination problem. The almost instantaneous visualization of results provided by the Java-based interface resulted in efficient and easy analyses. Although a performance comparison was not in mind, the evaluation of the same scenario using the original fortran code took three times as much total time (program run, evaluation of results and post-processing) as that using the Java simulation system.

Multilevel grid method for history matching multi-dimensional multi-phase reservoir models

Abstract The multilevel grid method (different from the multigrid method commonly used for accelerating the iterative solution process of linear algebraic equations) is used here to develop an efficient numerical algorithm for history matching multi-phase multi-dimensional reservoir models. The purpose of history matching is to identify the unknown oil reservoir structural parameters by matching the computed pressure values with measured pressure values at observation wells. One of the major problems in history matching is that the identified parameter distribution is very sensitive to the initial guess used to start the history matching process. The problem becomes worse as the number of grid points increases. With the multilevel grid, the history matching process starts on a coarse grid; the parameter distribution identified on the coarse grid is then interpolated onto a finer grid and used as a better initial guess to start the history matching on the finer grid. Although the history matching process becomes more sensitive to the initial guess as the number of grid points increases, the better initial guess obtained from the solution on the coarse grid offsets the increased sensitivity and improves the quality of the identified parameter distribution on the finer grid. The grid can be refined repeatedly until the desired resolution has been achieved. Numerical examples for two- and three-dimensional reservoir models are given in the paper, which demonstrate that the algorithm presented here is able to identify the reservoir absolute permeability distributions varying over the field by an order of magnitude with a constant initial guess deviating from the true distribution by two orders of magnitude. The use of the multilevel grid also reduces the computational complexity of the algorithm and speeds up the computations.

A self-adaptive time integration algorithm for solving partial differential equations

Non-uniform spatial grids are commonly used to resolve locally fast-changing physical phenomena in space. If a traditional explicit time integration scheme is used to advance solutions in the temporal dimension, the step size is restricted by the stability criterion, which is in turn dictated by the smallest grid spacing in the spatial dimensions. It turns out that the excessively small time step enforced by the smallest spatial grid spacing in a domain is usually unnecessary for most of the grid points with larger grid spacing. A new adaptive time integration method is introduced in this paper to improve the computational efficiency. The basic idea is to use different time step sizes at different spatial grid points. The stability criterion is still satisfied at all grid points by using different time step sizes. In this way, the time step size adjusts automatically based on the local spatial grid spacing. Complexity analysis and implementation details are also discussed in the paper. The non-linear Burgers equation is used in the numerical experiment. Both the complexity analysis and numerical computations demostrate significant improvement of computational efficiency.