Automatic mesh generation using the symmetric axis transformation of polygonal domains

Article Abstract:

An automatic method can be employed to generate finite element meshes for multiply connected planar domains with polygonal boundaries. To obtain a planar graph that partitions the given domain, the symmetric axis transform is used, which may introduce edges in the graph that are too long or short for generating good meshes. A sliver processing algorithm transforms the graph into another graph without the edges, which include symax, touching radius, full boundary edge and partial boundary edge. Additional nodes are placed on the graph's edges to obtain triangulation. The process is applied iteratively, which yields the final mesh. The method automatically increases the mesh density in regions of rapid change in shape, allows both local and global control of the mesh density and admits the imposition of node compatibility constraints along domain boundaries.

Systems analysis, Automation, Technical, Geometry, System Design, Scientific Research, Methods, Mesh Networks

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Algorithm transformation techniques for concurrent processors

Article Abstract:

Four algorithm transformation techniques for improving program execution on concurrent processing supercomputers are used to exploit existing parallelism in synchronous, iterative data-flow programs for signal processing supercomputing systems. Programming supercomputers for such computationally intensive operations requires partitioning the tasks in a way that optimizes concurrent processor utilization. Exploiting the concurrency in the programs can be done by three algorithm transformation techniques: program unfolding, retiming and index mapping. A look-ahead transformation algorithm can create additional concurrency in programs lacking sufficient parallelizable components. Functioning, implementation, and underlying equations of each transformation technique are discussed. Their applications to different supercomputer architectures are described.

Supercomputers, Supercomputer, Performance improvement (Computers), Multitasking (Computing), Optimization, Parallelism, Performance Improvement, Algorithm Analysis, Transforms, Concurrent Programming, technical, Parallel Algorithms

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Properties of the Qn-Matrix in Bilinear Transformation

Article Abstract:

A new general property relating two matrices of successive order for design of digital filters is proved. An example illustrates the theorem. A table gives the distribution of signs of eigenvalues for n between one and twenty.

Design, Matrices (Mathematics), Mathematical Proofs, Digital Filters, Matrices, Matrix Computations

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