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Vectorization is very important to the efficiency of computation in the popular
problem-solving environment Matlab. It is shown that a class of Runge-Kutta
methods investigated by Milne and Rosser that compute a block
of new values at each step are well-suited to vectorization. Local error estimates and
continuous extensions that require no additional function evaluations are derived.
A (7,8) pair is derived and implemented in a program BV78 that is shown to perform quite
well when compared to the well-known Matlab ODE solver ode45 which is
based on a (4,5) pair.
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Boundary value problems for ordinary differential equations (BVODES) occur in a great many practical situations and they are generally much harder to solve than initial value problems. Traditionally codes for BVODES did not take into account the conditioning of the problem and it was generally assumed that the problem being solved was well conditioned so that small local errors gave rise to correspondingly small global errors. Recently a new generation of codes which take account of conditioning has been developed. However most of these codes are based on a rather ad hoc approach with the need to choose several heuristics without any real guidance on how these choices can be made. In this paper we identify clearly which heuristics need to be chosen and we discuss different choices of monitor functions that are used in our codes. This has the important effect of unifying the various approaches that have recently been proposed. This in turn allows us, in the present paper, to introduce a new technique for computing the conditioning which is ideally suited to BVODES.
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A major problem in obtaining an efficient implementation of fully implicit Runge-Kutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with an approximate Jacobian matrix. The systems of linear equations of the modified Newton method can actually be solved approximately with a preconditioned linear iterative method. In this article we present a truly parallelizable preconditioner to the approximate Jacobian matrix. Its decomposition cost for a sequential or parallel implementation can be made equivalent to the cost corresponding to the implicit Euler method. The application of the preconditioner to a vector consists of three steps: two steps involve the solution of a linear system with the same block-diagonal matrix and one step involves a matrix-vector product. The preconditioner is asymptotically correct for the Dahlquist test equation. Some free parameters of the preconditioner can be determined in order to optimize certain properties of the preconditioned approximate Jacobian matrix.
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We consider linear systems with coefficient matrices having the ABD or the Bordered ABD (BABD) structures. These systems arise in the discretization of BVPs for ordinary and partial differential equations with separated and non-separated boundary conditions, respectively. We describe the cyclic reduction algorithm for the solution of BABD linear systems which allowed us to write the codes BABDCR and GBABDCR (the latter code is suitable for matrices with a more generic BABD structure). A comparison of the GBABDCR code with respect to the well-known sequential code COLROW on ABD linear systems is then analysed. We report some tests on an OpenMP Fortran 90 parallel version of the GBABDCR code and finally we discuss about the use of GBABDCR inside the BVP code BVPSOLVER.
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In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This allows to obtain efficient parallel extensions of many known matrix factorizations, and to derive, as a by-product, a unifying approach to the parallel solution of ODEs.
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This work concerns part of our project, devoted to the development of an agent-team-based Grid resource brokering and management system. Here, open issues that have to be addressed in the process, concern agent team preservation. In our earlier work it was suggested that this can be achieved through mirroring of key information. Here, we discuss in detail sources of useful information generated in the system (an agent team in particular) and consider which information should be mirrored, when and where, to increase long-term sustainability of an agent team.
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A generic infrastructural grid service for submission, management, and access to computing resource is described. It is suitable for interactive applications and on-demand computing with frequent usage of short jobs. The improved access to computing resources is achieved through allocation and maintenance of a pool of ready jobs, the size of which is dynamically adjusted to demand produced by applications. A set of APIs facilitates communication between the clients and worker jobs through a simple programming model.
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The paper describes system and program metrics used for load balancing algorithms for Java program execution in the SOAJA (Service Oriented Adaptative Java Applications) executive environment. This environment aims in maintaining design and execution of large scale computing tasks in complex networked Grid environments. SOAJA services provide means for static and dynamic load balancing with the use of special metrics obtained by Java object observation. SOAJA comprises mechanisms and algorithms for automatic placement and adaptation of application objects, in response to evolution of resource availability. Under control of SOAJA, parallel Java objects can be optimally allocated to Grid nodes before execution and next migrated at runtime to less loaded nodes to maintain the balance of loads of constituent JVMs. SOAJA mechanisms employ computation power metrics based on measurements of the idle time of processor nodes and communication bandwidth metrics for network resources based on statistical assessment of the existing traffic. Due to these mechanisms the granularity of computing and distribution of the application elements on the Grid platform can be optimally controlled.
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The transition from sequential computing to parallel computing represents the next turning point in the way software engineers design and write software. This paradigm shift leads the integration of parallel programming standards for high-end shared-memory machine architectures into desktop programming environments. In this paper we present a performance study of these new systems. We evaluate the performance of an OpenMP shared-memory programming model that is integrated into Microsoft Visual Studio C++ 2005 and Intel C++ compilers on a multicore processor. We benchmarked using the NAS OpenMP high-level applications benchmarks and the EPCC OpenMP low-level benchmarks. We report the basic timings and runtime profiles of each benchmark and analyze the running results.
