# Supercomputing about physical objects

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## Abstract

Scientific and technological advances in the next 5 to 10 years will make it feasible to create an integrated, interactive system for the design, manipulation and analysis of collections of physical objects. These advances will come in computing power through the mechanism of *parallel computation*, in *algorithms for geometry*, in *problem solving systems* to provide very high level user interfaces and in *graphics* to allow direct visualization of the behavior of the physical objects. In this paper we describe the project *Computing about Physical Objects* which is to explore the associated technical problems and to build prototypes of such systems. The focus here is upon the role of supercomputers in this area and, especially, their application to solving the partial differential equations that model many physical phenomena.

## Keywords

Physical Object Algebraic Curf Elliptic Partial Differential Equation Library Module Machine Selection## Preview

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## 6. References

- Abhyankar, S. S., (1983), Desingularization of plane curves. In
*Proc. Symp. in Pure Mathematics*, 40, 1–45.Google Scholar - Abhyankar, S. S., and C. Bajaj, (1987a), “Automatic rational parameterization of curves and surfaces I: Conics and conicoids”,
*Computer Aided Design*, 19,1, 11–14.Google Scholar - Abhyankar, S. S., and C. Bajaj, (1987b), “Automatic rational parameterization of curves and surfaces II: Cubics and cubicoids”,
*Computer Aided Design*, to appear.Google Scholar - Abhyankar, S. S., and C. Bajaj, (1987c), “Automatic parameterization of rational curves and surfaces III: Algebraic plane curves”, CSD-TR-619, Computer Science, Purdue University.Google Scholar
- Atallah, M., and C. Bajaj, (1987), “Efficient algorithms for common transversals”,
*Information Processing Letters*, 25, 2, 87–91.Google Scholar - Bajaj, C., (1985), “The Algebraic complexity of shortest paths in polyhedral spaces”. In
*Proc. 23rd Annual Allerton Conference on Communication, Control and Computing*, Univ. of Illinois, 510–517.Google Scholar - Bajaj, C., (1986), “An efficient parallel solution for shortest paths in 3-dimensions”. In
*Proc. 1986 IEEE International Conference on Robotics and Automation*, San Fransisco, 1897–1900.Google Scholar - Bajaj, C., (1987a), “Exact and approximate shortest path planning”. In
*Path Planning*, R. Franklin, ed., SIAM, to appear.Google Scholar - Bajaj, C., (1987b), “On algorithmic implicitization of rational algebraic curves and surfaces”, CSD-TR-681, Computer Science, Purdue University.Google Scholar
- Bajaj, C. and M. Kim, (1987a), “Generation of configuration space obstacles I: The case of a moving sphere”,
*IEEE J. of Robotics and Automation*, to appear.Google Scholar - Bajaj, C. and M. Kim, (1987b), “Generation of configuration space obstacles II: The case of moving algebraic surfaces”, CSD-TR-586, Computer Science, Purdue University.Google Scholar
- Bajaj, C. and M. Kim, (1987c), “Generation of configuration space obstacles III: The case of moving algebraic curves”,
*Algorithmica*, to appear.Google Scholar - Bajaj, C., and M. Kim, (1987d), “Compliant motion planning with geometric models”,
*Proc. of 3rd ACM Symposium on Computation Geometry*, 171–180.Google Scholar - Bajaj,C., and M. Kim, (1987e), “Convex decomposition of objects bounded by algebraic curves”, CSD-TR-677, Computer Science, Purdue University.Google Scholar
- Bajaj, C., and M. Kim, (1987f), “Convex hull of objects bounded by algebraic curves”, CSD-TR-697, Computer Science, Purdue University.Google Scholar
- Bajaj, C., C. Hoffmann and J. Hopcroft, (1987), “Tracing algebraic curves: Plane curves”, CSD-TR-637, Computer Science, Purdue University.Google Scholar
- Bajaj, C., C. Hoffmann, E. Houstis, J. Korb and J. Rice, (1987), “Computing about physical objects”, CSD-TR-696, Computer Science, Purdue University.Google Scholar
- Bajaj, C., C. Liu, and M. Wu, (1987), “A face area evaluation algorithm for solids in CSG representation”, CSD-TR-682, Computer Science, Purdue University.Google Scholar
- Bajaj, C., and T. Moh, (1987), “Generalized unfoldings for shortest paths”,
*Intl. J. of Robotics Research*, to appear.Google Scholar - Birkhoff, G. and R.E. Lynch, (1985), “Numerical solutions of elliptic problems”,
*SIAM Publications*, Philadelphia.Google Scholar - Boisvert, R.F., E.N. Houstis, and J.R. Rice, (1979), “A system for performance evaluation of partial differential equations software”.
*IEEE Trans. Software Engineering*,**5**, 418–425.Google Scholar - Dyksen, W.R., R.E. Lynch, J.R. Rice and E.N. Houstis, (1984), “The performance of the collocation and Galerkin methods with Hermite bi-cubics,”
*SIAM J. Numer. Anal.*,**21**, 695–715.Google Scholar - Dyksen, W.R. and C.J. Ribbens, (1987), “Interactive ELLPACK: An interactive problem solving environment for elliptic partial differential equations”,
*ACM Trans. Math. Software*,**13**, to appear.Google Scholar - Hoffmann, C. and J. Hopcroft, (1985), “Automatic surface generation in computer aided design”,
*The Visual Computer*,**1**, 92–100.Google Scholar - Hoffmann, C. and J. Hopcroft, (1986), “Quadratic blending surfaces”,
*Comp. Aided Design*, 18, 301–306.Google Scholar - Hoffmann, C. and J. Hopcroft, (1987a), “Geometric ambiguities in boundary representations”,
*Comp. Aided Design*, 19, 141–147.Google Scholar - Hoffmann, C. and J. Hopcroft, (1987b), “The potential method for blending surfaces and corners”, in
*Geometric Modeling*, G. Farin, ed., SIAM, 347–366.Google Scholar - Hoffmann, C. and J. Hopcroft, (1987), “Simulation of physical systems from geometric models”, special issue,
*IEEE J. of Robotics and Automation*, (June).Google Scholar - Hoffmann, C., J. Hopcroft, and M. Karasick, (1986), “Boolean operations on boundary representations of polyhedral objects”, in preparation.Google Scholar
- Houstis, C.E., E.N. Houstis and J.R. Rice, (1984), “Partitioning and allocation of PDE computations in distributed systems”. In
*PDE Software: Modules, Interfaces and Systems*, (Engquist and Smedsaas, eds.), North-Holland, 67–85.Google Scholar - Houstis, C.E., E.N. Houstis and J.R. Rice, (1987), “Partitioning PDE computations: Methods and performance evaluations”,
*Journal Parallel Computing*, to appear.Google Scholar - Houstis, C.E., E.N. Houstis, J.R. Rice and M. Samartzis, “Benchmarking of bus multiprocessor hardware for large scale scientific computing”. In
*Advances in Computer Methods for Partial Differential Equations, VI*, (Stepleman and Vishnevetsky, eds), IMACS, 136–141.Google Scholar - Houstis, E.N., W.F. Mitchell, and J.R. Rice, (1985a), “Collocation software for second order elliptic partial differential equations”,
*ACM Trans. Math. Software*,**11**, 379–412.Google Scholar - Houstis, E.N., W.F. Mitchell, and J.R. Rice, (1986b), “Algorithm 638 GENCOL: Collocation on general domains with bicubic Hermite polynomials”,
*ACM Trans. Math. Software*,**11**, 416–418.Google Scholar - Houstis, E.N., W.F. Mitchell and J.R. Rice, (1985c), “Algorithm 638, INTCOL and HERMCOL: Collocation on rectangular domains with bicubic Hermite polynomials”,
*ACM Trans. Math. Software*,**11**, 416–418.Google Scholar - Houstis, E.N., M.A. Vavalis and J.R. Rice, (1987), “Parallelization of a new class of cubic spline collocation methods”. In
*Advances in Computer Methods for Partial Differential Equations, VI*, (Stepleman and Vishnevetsky, eds), IMACS, 167–174.Google Scholar - Houstis, E.N., E.A. Vavalis and J.R. Rice, (1988), “Convergence of an
*O*(*h*^{4}) cubic spline collocation method for elliptic partial differential equations”,*SIAM J. Num. Anal.*, to appear.Google Scholar - Lynch, R.E. and Rice, J.R., (1978), “High accuracy finite difference approximation to solutions of elliptic partial differential equations”,
*Proc. Nat. Acad. Sci.*,**75**, 2541–2544.Google Scholar - Marinescu, D.C. and J.R. Rice, (1987a), “Domain oriented analysis of PDE splitting algorithms”,
*J. Info. Sci.*,**42**, to appear.Google Scholar - Marinescu, D.C. and J.R. Rice, (1987b), “Analysis and modeling of Schwarz splitting algorithms for elliptic PDE's”. In
*Advances in Computer Methods for Partial Differential Equations, VI*(Stepleman and Vishnevetsky, eds), IMACS, 1–6.Google Scholar - McFaddin, H.S. and J.R. Rice, (1987), “Parallel and vector problems on the FLEX/32”, CSD-TR-661, Computer Science, Purdue University.Google Scholar
- Ribbens, C., (1986), “Domain mappings: A tool for the development of vector algorithms for numerical solutions of partial differential equations”, Ph.D. Thesis, Purdue University.Google Scholar
- Ribbens, C.J. and J.R. Rice, (1986), “Realistic PDE solutions for nonrectangular domains”, CSD-TR-639, Computer Science, Purdue University.Google Scholar
- Rice, J.R., (1985), “Problems to test parallel and vector languages”, CSD-TR-516, Computer Science, Purdue University.Google Scholar
- Rice, J.R., (1986a), “Parallelism in solving PDEs”,
*Proc. Fall Joint Compiler Conf.*, IEEE, 540–546.Google Scholar - Rice, J.R., (1986b), “Multi-FLEX machines: Preliminary report”, CSD-TR-612, Computer Science, Purdue University.Google Scholar
- Rice, J.R., (1986c), “Design of a tensor product population of PDE problems”, CSD-TR-628, Computer Science, Purdue University.Google Scholar
- Rice, J., (1986), “Adaptive tensor product grids for singular problems”. In
*Algorithms for the Approximation of Functions and Data*, (J. Mason, ed.), Oxford University Press.Google Scholar - Rice, J.R., (1987b), “ELLPACK: An evolving problem solving environment”. In
*Problem Solving Environments for Scientific Computing*(B. Ford, ed.) North-Holland, to appear.Google Scholar - Rice, J.R., (1987c), “Parallel methods for partial differential equations”. In
*The Characteristics of Parallel Computations*, (Jamieson, Gannon, Douglass, eds), MIT Press, Chapter 8, 209–231.Google Scholar - Rice, J.R., (1987d), “Using supercomputers today and tomorrow”. In
*Proc. Fourth Army Conf. Appl. Math. Computing*, 1333–1343.Google Scholar - Rice, J.R., and R.F. Boisvert, (1985), “Solving elliptic problems using ELLPACK”, Springer Verlag.Google Scholar
- Rice, J.R., W.R. Dyksen, E.N. Houstis, and C.J. Ribbens, (1986), “ELLPACK status report”. CSD-TR-579, Computer Science, Purdue University.Google Scholar
- Rice, J.R., Houstis, E.N. and Dyksen, W.R., (1981), “A population of linear, second order, elliptic partial differential equations on rectangular domains, Parts 1 and 2”,
*Math. Comp*,**36**, 475–484.Google Scholar - Rice, J.R., (1984a), “Numerical computation with general two dimensional domains”.
*ACM Trans. Math. Software*,**10**, 443–452.Google Scholar - Rice, J.R., (1984b), “Algorithm 624: A two dimensional domain processor”.
*ACM Trans. Math. Software*,**10**, 453–562.Google Scholar