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.
Research supported in part by Strategic Defense Initiative grant ARO DAA929-83-K-0026.
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6. References
Abhyankar, S. S., (1983), Desingularization of plane curves. In Proc. Symp. in Pure Mathematics, 40, 1–45.
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.
Abhyankar, S. S., and C. Bajaj, (1987b), “Automatic rational parameterization of curves and surfaces II: Cubics and cubicoids”, Computer Aided Design, to appear.
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.
Atallah, M., and C. Bajaj, (1987), “Efficient algorithms for common transversals”, Information Processing Letters, 25, 2, 87–91.
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.
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.
Bajaj, C., (1987a), “Exact and approximate shortest path planning”. In Path Planning, R. Franklin, ed., SIAM, to appear.
Bajaj, C., (1987b), “On algorithmic implicitization of rational algebraic curves and surfaces”, CSD-TR-681, Computer Science, Purdue University.
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.
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.
Bajaj, C. and M. Kim, (1987c), “Generation of configuration space obstacles III: The case of moving algebraic curves”, Algorithmica, to appear.
Bajaj, C., and M. Kim, (1987d), “Compliant motion planning with geometric models”, Proc. of 3rd ACM Symposium on Computation Geometry, 171–180.
Bajaj,C., and M. Kim, (1987e), “Convex decomposition of objects bounded by algebraic curves”, CSD-TR-677, Computer Science, Purdue University.
Bajaj, C., and M. Kim, (1987f), “Convex hull of objects bounded by algebraic curves”, CSD-TR-697, Computer Science, Purdue University.
Bajaj, C., C. Hoffmann and J. Hopcroft, (1987), “Tracing algebraic curves: Plane curves”, CSD-TR-637, Computer Science, Purdue University.
Bajaj, C., C. Hoffmann, E. Houstis, J. Korb and J. Rice, (1987), “Computing about physical objects”, CSD-TR-696, Computer Science, Purdue University.
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.
Bajaj, C., and T. Moh, (1987), “Generalized unfoldings for shortest paths”, Intl. J. of Robotics Research, to appear.
Birkhoff, G. and R.E. Lynch, (1985), “Numerical solutions of elliptic problems”, SIAM Publications, Philadelphia.
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.
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.
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.
Hoffmann, C. and J. Hopcroft, (1985), “Automatic surface generation in computer aided design”, The Visual Computer, 1, 92–100.
Hoffmann, C. and J. Hopcroft, (1986), “Quadratic blending surfaces”, Comp. Aided Design, 18, 301–306.
Hoffmann, C. and J. Hopcroft, (1987a), “Geometric ambiguities in boundary representations”, Comp. Aided Design, 19, 141–147.
Hoffmann, C. and J. Hopcroft, (1987b), “The potential method for blending surfaces and corners”, in Geometric Modeling, G. Farin, ed., SIAM, 347–366.
Hoffmann, C. and J. Hopcroft, (1987), “Simulation of physical systems from geometric models”, special issue, IEEE J. of Robotics and Automation, (June).
Hoffmann, C., J. Hopcroft, and M. Karasick, (1986), “Boolean operations on boundary representations of polyhedral objects”, in preparation.
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.
Houstis, C.E., E.N. Houstis and J.R. Rice, (1987), “Partitioning PDE computations: Methods and performance evaluations”, Journal Parallel Computing, to appear.
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.
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.
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.
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.
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.
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.
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.
Marinescu, D.C. and J.R. Rice, (1987a), “Domain oriented analysis of PDE splitting algorithms”, J. Info. Sci., 42, to appear.
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.
McFaddin, H.S. and J.R. Rice, (1987), “Parallel and vector problems on the FLEX/32”, CSD-TR-661, Computer Science, Purdue University.
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.
Ribbens, C.J. and J.R. Rice, (1986), “Realistic PDE solutions for nonrectangular domains”, CSD-TR-639, Computer Science, Purdue University.
Rice, J.R., (1985), “Problems to test parallel and vector languages”, CSD-TR-516, Computer Science, Purdue University.
Rice, J.R., (1986a), “Parallelism in solving PDEs”, Proc. Fall Joint Compiler Conf., IEEE, 540–546.
Rice, J.R., (1986b), “Multi-FLEX machines: Preliminary report”, CSD-TR-612, Computer Science, Purdue University.
Rice, J.R., (1986c), “Design of a tensor product population of PDE problems”, CSD-TR-628, Computer Science, Purdue University.
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.
Rice, J.R., (1987b), “ELLPACK: An evolving problem solving environment”. In Problem Solving Environments for Scientific Computing (B. Ford, ed.) North-Holland, to appear.
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.
Rice, J.R., (1987d), “Using supercomputers today and tomorrow”. In Proc. Fourth Army Conf. Appl. Math. Computing, 1333–1343.
Rice, J.R., and R.F. Boisvert, (1985), “Solving elliptic problems using ELLPACK”, Springer Verlag.
Rice, J.R., W.R. Dyksen, E.N. Houstis, and C.J. Ribbens, (1986), “ELLPACK status report”. CSD-TR-579, Computer Science, Purdue University.
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.
Rice, J.R., (1984a), “Numerical computation with general two dimensional domains”. ACM Trans. Math. Software, 10, 443–452.
Rice, J.R., (1984b), “Algorithm 624: A two dimensional domain processor”. ACM Trans. Math. Software, 10, 453–562.
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Rice, J.R. (1988). Supercomputing about physical objects. In: Houstis, E.N., Papatheodorou, T.S., Polychronopoulos, C.D. (eds) Supercomputing. ICS 1987. Lecture Notes in Computer Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18991-2_26
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DOI: https://doi.org/10.1007/3-540-18991-2_26
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