Fixed Point Computation and Parallel Algorithms for Solving Wave Equations

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Publication Type technical report
School or College College of Engineering
Department Computing, School of
Creator Tsay, Chey-Woei
Title Fixed Point Computation and Parallel Algorithms for Solving Wave Equations
Date 1994
Description This dissertation is concerned with two problems: fixed-point computation and parallel algorithms for solving wave equations. Many problems can be formulated as fixed-point problems, which is to solve the equations of the form f(x) - x = 0. We develop efficient algorithms and establish complexity results for such fixed-point computations. For univariate functions, we demonstrate Fixed Point Envelope (FP-EN) algorithms and prove that they minimize the number of function evaluations for computing an approximation to within a prescribed absolute error tolerance. For multivariate contractive functions, we exhibit a Fixed Point Ellipsoid (FP-EL) algorithm. This algorithm is much more efficient than the well-known simple iteration algorithm. We also show an upper bound on the number of function evaluations for this case. For multivariate noncontractive functions, we prove that the complexity is infinite whenever the error tolerance is less than 0.5. As the second problem, we consider the acoustic wave equation and the elastic wave equation that are frequently used in seismology. We develop parallelized finite difference algorithms for solving these equations. This is done by dividing the computational domain into subdomains and then by assigning a processor to each subdomain for computing and storing local grid data. We discuss parallel algorithms on three computing networks: processor arrays, rings, and meshes, with emphasis on the part of communication and synchronization. Finally, we demonstrate that our implementations on transputer linear arrays achieve linear speedup.
Type Text
Subject fixed point computation; parallel algorithm; fixed point envelope; fixed point ellipsoid; wave equation; processor array; transputer; linear array
Subject LCSH Fixed point theory; Parallel processing (Electronic computers); Wave equation
Language eng
Bibliographic Citation Tsay, C. (1994). Fixed Point Computation and Parallel Algorithms for Solving Wave Equations.
Series University of Utah Computer Science Technical Report
Relation is Part of ARPANET
Format Medium application/pdf
Format Extent 67,222,126 bytes
File Name Tsay-Fixed_Point_Computation.pdf
Conversion Specifications Original scanned with Kirtas 2400 and saved as 400 ppi uncompressed TIFF. PDF generated by Adobe Acrobat Pro X for CONTENTdm display
ARK ark:/87278/s6mw4jc4
Setname ir_computersa
Date Created 2016-05-26
Date Modified 2016-05-31
ID 102378
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