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NUMERICAL ANALYSIS TITLES
     -- Volume 3, Number 2, Part 1 of 3
     -- August 27, 1985
==================================================

Please note:  Due to its length, this list is
              being distributed in 3 parts, each
              part is about 7 pages in length.

##### AT&T BELL LABORATORIES #####
For copies of these reports, send mail to
   {ucbvax,ihnp4}!research!wmc
or
   wmc.btl@csnet-relay
or
   na.coughran@su-score
or
   Bill Coughran
   AT&T Bell Labs 2C419
   Murray Hill, NJ 07974
   (201) 582-6619
###################

[1] R. E. Bank, W. M. Coughran, Jr., W. Fichtner,
    D. J. Rose, and R. K. Smith,

    COMPUTATIONAL ASPECTS OF SEMICONDUCTOR DEVICE SIMULATION

    NAMs 85-3

In this chapter, we present an overview of the numerical
techniques used to solve the coupled system of nonlinear
partial differential equations that model the behavior of
semiconductor devices.  These methods have been incorporated
into our device simulation package which has been success-
fully used to model complex device structures in two and
three space dimensions for both steady-state and transient
conditions.
---------------

[2] R. E. Bank, W. M. Coughran, Jr., W. Fichtner,
    E. H. Grosse, D. J. Rose, R. K. Smith,

    TRANSIENT SIMULATION OF SILICON DEVICES AND CIRCUITS

    NAMs 85-8

In this paper, we present an overview of the physical prin-
ciples and numerical methods used to solve the coupled sys-
tem of nonlinear partial differential equations that model
the transient behavior of silicon VLSI device structures.
We also describe how the same techniques are applicable to
circuit simulation.  A composite linear multistep formula is
introduced as the time-integration scheme.  Newton-iterative
methods are exploited to solve the nonlinear equations that
arise at each time step.  We also present a simple data
structure for nonsymmetric matrices with symmetric nonzero
structures that facilitates iterative or direct methods with
substantial efficiency gains over other storage schemes.
Several computational examples, including a CMOS latchup
problem, are presented and discussed.
---------------

##### CORNELL #####

[3] Franklin T. Luk and Sanzheng Qiao

    A fast but unstable orthogonal triangularization technique
    for Toeplitz matrices

    EE-CEG-85-5


Address: School of Electrical Engineering
         Cornell University
         Ithaca, NY 14863

    < No Abstract >

Submitted by: Frank Luk (luk%tesla@cornell.csnet)
Obtainable from:
  Frank Luk
  Cornell University
  Ithaca, New York  14853
---------------

[4] Franklin T. Luk 

    Algorithm-based Fault Tolerance for Parallel
    Matrix Equation Solvers 

    EE-CEG-85-2
    School of Electrical Engineering, Cornell University 
    Ithaca, New York  14853
    June 1985

We examine the checksum schemes of Abraham et al. for 
the computation of the LU-factorization using a multiprocessor array.
Their methods are very efficient for detecting a transient error,
but quite expensive for correcting it
due to the need for a computation rollback.
In this paper, we show how to avoid the rollback and how to implement pivoting.
We also introduce a new checksum method 
for solving triangular sets of linear equations.

Obtainable from: Frank Luk, above.
---------------

##### COURANT INSTITUTE #####

[5] O. McBryan

    Computational Methods for  Discontinuities in  Fluids

    Lectures in Applied Mathematics
    vol. 22, AMS, Providence, 1985.

    < No Abstract >

Submitted by: Oliver McBryan (mcbryan@nyu.arpa)
Obtainable from:
    Oliver McBryan
    Courant Institute
    251 Mercer St
    New York, NY 10012
---------------

[6] O. McBryan and E. Van de  Velde

    Parallel Algorithms for Elliptic Equations

    Proceedings of the
    1984 ARO Novel Computing Environments Conference
    Stanford University, SIAM , to appear.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[7] O. McBryan, E. Van de Velde, and P.  Vianna

    Parallel Algorithms for Elliptic and Parabolic Equations

    Proceedings of the Conference on Parallel Computations
    in Heat Transfer and Fluid Flows
    University of Maryland, November 1984.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[8] O. McBryan

    Using CRAY super-computers as Attached Processors

    Courant Institute Preprint, 1985.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[9] O. McBryan

    State of the Art of Multiprocessors in Scientific Computation

    Proceedings of European
    Weather Center Conference on Multiprocessors
    Reading, England, Dec 1984, to appear.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[10] O. McBryan and E. Van de Velde

    Parallel Algorithms for Elliptic Equation
    Solution on the HEP Computer

    Proceedings of the First HEP Conference
    University of Oklahoma, March 1985.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[11] O. McBryan and E. Van de Velde

    Parallel  Algorithms for Elliptic Equations

    to appear in  Commun. Pure and Appl. Math., Feb 1985.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[12] O. McBryan and E. Van de Velde

    Elliptic  Equation Algorithms  on  Parallel Computers

    Proceedings of the Conference on Parallel Computers
    and Partial Differential Equations,
    Commun. in Applied  Numerical Methods,
    University of Texas, Austin, March 1985, to appear.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[13] J. Glimm, B. Lindquist, O. McBryan, and G. Tryggvason

     Sharp and Diffuse Fronts in Oil Reservoirs:
     Front Tracking and Capillarity

     Proceedings of the Houston SPE/SIAM meeting
     on Mathematics of Reservoir Simulation,
     SIAM, to appear, Feb. 1985.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------

[14] J. Glimm and O. McBryan

    A Computational Model for Interfaces

    Courant Institute Preprint, 1985.

    < No Abstract >
 
Obtainable from: O. McBryan, above.
---------------


[15] James W. Demmel and Bo Kagstrom

    Computing Stable Eigendecompositions of Matrix Pencils

    Technical Report # 163
    Computer Science Department
    Courant Institute
    May, 1985

We discuss how to compute an eigendecomposition of a matrix pencil
A-zB when A and B are only known to within a tolerance epsilon. When
A-zB is regular (i.e. det(A-zB) is not identically zero) we show how
to partition the spectrum and eigenspaces of A-zB into clusters which
vary smoothly as A-zB varies within a ball of radius epsilon. When
A-zB is singular (a case of interest in systems theory) so that the
structures we wish to compute are nongeneric, we show that certain spaces 
and eigenvalues of the pencil vary smoothly if A-zB varies along a lower 
dimensional surface as well as within a ball of radius epsilon.  This 
result implies that the usual algorithms for analyzing singular pencils
generally compute accurate eigenvalues and spaces. We apply this result 
by computing perturbation bounds for the controllable subspace and 
uncontrollable modes of a system dx/dt = Cx + Du.

Submitted by:    James Demmel (demmel.csd2@nyu)
Obtainable from:
  James Demmel  
  Courant Institute
  251 Mercer Str.
  New York, NY   10012
---------------

[16] Jonathan Goodman, Robert Kohn, and Luis Reyna

    A Numerical Study of a Relaxed Variational Problem

We present the numerical solution of an optimization problem that arises
in two phase flow, and in the design of a beam out of two different materials
in given proportion for optimum torsional rigidity.  The problem is to
minimize a Dirichlet integral over all possible functions and over all possible
subdomains of a given area.  Minimizing over functions with the subdomain fixed
would lead to a second order elliptic equation with discontinuous coefficients.
A naive (but very plausible) algorithm based directly on this formulation is
shown to have "premature termination" at points that are not even stationary
points.  It is known that problems like this often do not have "classical"
solutions.  Rather, there are "weak" or "relaxed" solutions that involve
microscopic mixing of the two materials.  Application of homogenization theory
gives a relaxed minimization problem that can numerically be solved.  We used a
variational multigrid proceedure to get high resolution (256 x 256) in
reasonable time on a VAX-780.  The numerical results show that the region of
microscopic mixing can occupy about 15% of the region in some cases.

Submitted by: Jonathan Goodman (goodnan@nyu-acf1.csnet)
Obtainable from:
  Jonathan Goodman
  Courant Institute of Mathematical Sciences
  251 Mercer St.
  New York, New York, 10012
---------------

[17] Jonathan Goodman, Robert Kohn, and Luis Reyna

     A Numerical Study of a Relaxed Variational Problem

We present the numerical solution of an optimization problem that arises
in two phase flow, and in the design of a beam out of two different materials
in given proportion for optimum torsional rigidity.  The problem is to
minimize a Dirichlet integral over all possible functions and over all possible
subdomains of a given area.  Minimizing over functions with the subdomain fixed
would lead to a second order elliptic equation with discontinuous coefficients.
A naive (but very plausible) algorithm based directly on this formulation is
shown to have "premature termination" at points that are not even stationary
points.  It is known that problems like this often do not have "classical"
solutions.  Rather, there are "weak" or "relaxed" solutions that involve
microscopic mixing of the two materials.  Application of homogenization theory
gives a relaxed minimization problem that can numerically be solved.  We used a
variational multigrid proceedure to get high resolution (256 x 256) in
reasonable time on a VAX-780.  The numerical results show that the region of
microscopic mixing can occupy about 15% of the region in some cases.

Obtainable from J. Goodman, above
---------------

[18] Jonathan Goodman

    Convergence of the Random Vortex Method

The random vortex method, introduced by Chorin, was intended to compute
high Reynolds number incompressible flows in 2 or 3 dimensions.  We prove
that the method converges (with probability one) for smooth flows without
boundaries in two dimensions.  The error bounds are independent of the
viscosity.  The proof relies on the form of smoothing (replacing vortex
points by vortex blobs) introduced by Hald in his convergence proof for
the (non-random) vortex method for the incompressible Euler equations in
2 dimensions.

Obtainable from J. Goodman, above
---------------

##### EMORY #####

[19] Henry Wolkowicz and Phil Smith

    A NONLINEAR EQUATION FOR LINEAR PROGRAMMING

    Research Report 16
    Emory University

We present a characterization of the 'normal' optimal solution of the linear
programming problem. This characterization involves the solution of 
m piecewise linear equations in m unknowns.

Submitted by: Henry Wolkowicz
  csnet:    henry@emory
  bitnet:   henry_wolkowicz@uqv-mts.bitnet
  uucp:     alberta!uqv-mts!sunn
                     emory!henry
Obtainable from:
  Henry Wolkowicz
  Department of Mathematics and Computer Science
  Emory University
  Atlanta, Georgia 30322
---------------