16 research outputs found
On the Lyapunov Second Method for Data Measurable in Time
In this paper the authors study time dependent Lyapunov functions for nonautonomous systems described by differential inclusions. In particular it is shown that Lyapunov functions are viscosity supersolutions of a Hamilton-Jacobi equation. For this aim a new viability theorem for differential inclusions with time dependent state constraints is proved. The viability conditions are formulated both using contingent cones and in a dual way, using subnormal cones (negative polar of contingent cone)
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Nonlinear explicit transient finite element analysis on the Intel Delta
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented
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Nonlinear explicit transient finite element analysis on the Intel Delta
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented
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The Advanced Software Development and Commercialization Project
This is the first of a series of reports pertaining to progress in the Advanced Software Development and Commercialization Project, a joint collaborative effort between the Center for Supercomputing Research and Development of the University of Illinois and the Computing and Telecommunications Division of Argonne National Laboratory. The purpose of this work is to apply techniques of parallel computing that were pioneered by University of Illinois researchers to mature computational fluid dynamics (CFD) and structural dynamics (SD) computer codes developed at Argonne. The collaboration in this project will bring this unique combination of expertise to bear, for the first time, on industrially important problems. By so doing, it will expose the strengths and weaknesses of existing techniques for parallelizing programs and will identify those problems that need to be solved in order to enable wide spread production use of parallel computers. Secondly, the increased efficiency of the CFD and SD codes themselves will enable the simulation of larger, more accurate engineering models that involve fluid and structural dynamics. In order to realize the above two goals, we are considering two production codes that have been developed at ANL and are widely used by both industry and Universities. These are COMMIX and WHAMS-3D. The first is a computational fluid dynamics code that is used for both nuclear reactor design and safety and as a design tool for the casting industry. The second is a three-dimensional structural dynamics code used in nuclear reactor safety as well as crashworthiness studies. These codes are currently available for both sequential and vector computers only. Our main goal is to port and optimize these two codes on shared memory multiprocessors. In so doing, we shall establish a process that can be followed in optimizing other sequential or vector engineering codes for parallel processors