Send mail to:    mgnet@cs.yale.edu             for the digests or bakeoff
Current editor:  Craig Douglas                 douglas-craig@cs.yale.edu
Anonymous ftp repository:    casper.cs.yale.edu (128.36.12.1)

World Wide Web:  file://na.cs.yale.edu/pub/mgnet/www/mgnet.html

Today's editor:  Craig Douglas (douglas-craig@cs.yale.edu)

Volume 4, Number 8 (approximately August 31, 1994)

Today's topics:

World Wide Web (WWW) Information
3D Vectorized Solvers
Fortran-90 Multigrid Solvers

-------------------------------------------------------

Date: Mon, 8 Aug 94 10:12:45 EDT
From: Craig Douglas
Subject: World Wide Web (WWW) Information

I finally got around to putting MGNet onto the web.  You can access it by
using the command

Mosaic file://na.cs.yale.edu/pub/mgnet/www/mgnet.html &

(substitute whatever works for you for Mosaic).  At the moment, it is pretty
simple.  I can only brag about the Copper Mountain '95 button, which I scanned
off of a postcard.  The interface will improve, hopefully, over time.

-------------------------------------------------------

Date: Sun, 14 Aug 94 16:05:04 METDST
From: Mathieu Pourquie
Subject: 3D Vectorized Solvers

Hi,

I am Mathieu Pourquie, working in Wolfgang Rodi's group in Karlsruhe, Germany.
We work, among other things, on the subject of turbulent flow simulation in
general coordinates.  People overhere are working on a multi-grid version of
the model right now.  Of course, we are interested in a membership of the
multi-grid group in Yale.

Perhaps I may take this opportunity to ask some question:  besides a general
interest in multi-grid for Navier-Stokes solvres, we are looking at this
moment for a (fast, vectorizing) 3-D, 7-point Poisson solver; since the
equation may not be separable, multi-grid seems very attrative.  Because we
need the solution of the Poisson equation to make the flow field divergence
free on discrete level, we prefer to prescribe the equation to be solved in
algebraic form on the finest grid (i.e., we like to give the coefficients
a,b,c,d,e,f,g, in the molecule; a driver approximating a continuous equation
may not result in precisely the equations we want to solve).

f
| .e
|.
a--- d----c
. |
.  |
b   g

Do you know of any?

Mit freundlichen Gr"ussen, Mathieu Pourquie

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@@
- Mathieu Pourquie         ------------voice:(0721) - 608 3533 -
- Institut f"ur Hydromechanik            FAX:(0721) - 608 2202 -
- University of Karlsruhe                                      -
- Kaiserstrasse 12                                             -
- 76128 Karlsruhe                                              -
- Germany                                                      -
-                                                              -
-   Internet: mathieu@ifh-hp6.bau-verm.uni-karlsruhe.de           -
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++@@

-------------------------------------------------------

Date: Thu, 1 Sep 1994 15:55:27 --100
From: rongen@prl.philips.nl (rongen pmj)
Subject: Multigrid and Fortran 90

Philips Research Lab.
Eindhoven, Sept. 1 1994

Dear Dr. Douglas,

While searching several directories and files on mgnet, I noticed
several of your papers on MADPACK and I also noticed that much of the
currently available MG-software on the public net is either written
in Fortran 77 or in C.

As you probably know, there is a new Fortran standard since 1991
and at our laboratory we already have several good Fortran-90 compilers
running on our computers.

Now my question is:  does there also exist MG-software written in the
new Fortran-90 language and if so, is it publicly available on the net?
Is there anyhow some address with general numerical software written in this
new language?
I would appreciate it if you could answer my questions, because I
personally believe that Fortran-90 is a much better language to program in
than Fortran 77.

With kind regards,

Peter M.J. Rongen
Philips Research Labs.
Prof. Holstlaan 4
5656 AA Eindhoven
The Netherlands.

E-mail : rongen@prl.philips.nl

Editor's Note:  I am not aware of any publically available Fortran-90
-------------   multigrid solvers.  It would be pretty easy for someone to
rewrite the C codes in Madpack5 into Fortran-90, however.

If anyone has a Fortran-90 code and is willing to put it
on MGNet, there is always space available...

-------------------------------------------------------

Date: Thu, 1 Sep 1994 21:06:20 +0200
From: gmap21@f1ibmsv2.gmd.de (Hubert Ritzdorf)

Hi,

I send you a list of publications of the GMD which are not already contained
in the MGNet BibTeX Database file mgnet.bib''. I have tried to specify the

Hubert

(Hubert.Ritzdorf@gmd.de)

Editor's Note:  The published works will be entered into the bibliography
-------------   shortly.  Here is a short LaTeX file that will print what
was sent to me.  Blame me if it does not print correctly.

\documentstyle[12pt]{siam}
\sloppy

\begin{document}
\bibliographystyle{siam}

\nocite{SRM_de_Barros_1989a}
\nocite{SRM_de_Barros_DPDee_FDickstein_1990a}
\nocite{SRM_de_Barros_JRBates_FHMSemazzi_RWHiggins_1990b}
\nocite{SRM_de_Barros_1991a}
\nocite{RBenAv_MHarmatz_PGLauwers_SSolomon_1993a}
\nocite{RBenAv_ABrandt_MHarmatz_EKatznelson_PGLauwers_SSolomon_KWolowesky_1991b}
\nocite{FBrakhagen_TWFogwell_1991a}
\nocite{FBrakhagen_TWFogwell_1991b}
\nocite{FBrakhagen_TWFogwell_1992a}
\nocite{JCanu_JLinden_1992a}
\nocite{JCanu_HRitzdorf_1993a}
\nocite{EDick_JLinden_1989a}
\nocite{EDick_JLinden_1989b}
\nocite{CFrohnSchauf_1992a}
\nocite{UGaertel_1989a}
\nocite{UGaertel_MGriebel_WHuber_HSchwichtenberg_1993a}
\nocite{UGaertel_WJoppich_HRitzdorf_ASchueller_BSteckel_KStueben_1993a}
\nocite{UGaertel_WJoppich_ASchueller_HSchwichtenberg_UTrottenberg_GWinter_1993a}
\nocite{UGaertel_AKrechel_ANiestegge_HJPlum_1991a}
\nocite{UGaertel_KRessel_1991a}
\nocite{MHarmatz_PGLauwers_RBenAv_ABrandt_EKatznelson_SSolomon_KWolowesky_1991a}
\nocite{WJoppich_1991b}
\nocite{WJoppich_SMijalkovic_1993a}
\nocite{PGLauwers_1991a}
\nocite{PGLauwers_1993a}
\nocite{MLemke_1993a}
\nocite{JLinden_GLonsdale_HRitzdorf_ASchueller_1992a}
\nocite{JLinden_GLonsdale_HRitzdorf_ASchueller_1992b}
\nocite{JLinden_GLonsdale_BSteckel_KStueben_1989a}
\nocite{JLinden_KStueben_1992a}
\nocite{GLonsdale_ASchueller_1991a}
\nocite{GLonsdale_ASchueller_1991b}
\nocite{RALorentz_1990a}
\nocite{YLuh_1993a}
\nocite{OMcBryan_UTrottenberg_1989a}
\nocite{KDOertel_KStueben_1988a}
\nocite{CWOosterlee_HRitzdorf_ASchueller_BSteckel_1994a}
\nocite{CWOosterlee_HRitzdorf_ASchueller_BSteckel_1994b}
\nocite{CWOosterlee_PWesseling_1994a}
\nocite{OPaetzold_1989a}
\nocite{HRitzdorf_ASchueller_BSteckel_KStueben_1994a}
\nocite{HRitzdorf_KStueben_1993a}
\nocite{ASchueller_1990a}
\nocite{ASchueller_1993a}
\nocite{HSchwichtenberg_GWinter_1991a}
\nocite{RStrasser_GNanz_WJoppich_1993}

\begin{thebibliography}{10}

\bibitem{RBenAv_ABrandt_MHarmatz_EKatznelson_PGLauwers_SSolomon_KWolowesky_199%
1b}
{\sc R.~Ben-Av, A.~Brandt, M.~Harmatz, E.~Katznelson, P.~Lauwers, S.~Solomon,
and K.~Wolowesky}, {\em {Fermion simulations using parallel transported
multigrid}}, Phys.Lett., B253 (1991).

\bibitem{RBenAv_MHarmatz_PGLauwers_SSolomon_1993a}
{\sc R.~Ben-Av, M.~Harmatz, P.~Lauwers, and S.~Solomon}, {\em
{Parallel-Transported Multigrid for inverting the Dirac-Operator: variants of
the method and their efficiency }}, Nucl. Phys., B 405 (1993), p.~623.
\newblock {Also published as Arbeitspapiere der GMD 674}.

\bibitem{FBrakhagen_TWFogwell_1991b}
{\sc F.~Brakhagen and T.~W. Fogwell}, {\em {Multigrid for the Fully Implicit
Formulation of the Equations for Multiphase Flow in Porous Media}}, in
{Multigrid Methods: Special Topics and Application II}, W.~Hackbusch and
U.~Trottenberg, eds., {GMD--Studie 189, Gesellschaft f{\"u}r Mathematik und
Datenverarbeitung, Sankt Augustin}, May 1991, pp.~31 -- 42.

\bibitem{FBrakhagen_TWFogwell_1991a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em {Multigrid Methods
for Systems of Partial Differential Equations with Discontinuous
Coefficients.}}, in {Third International Conference on Hyperbolic Problems,
Theory, Numerical Methods and Applications}, B.~Engquist and B.~Gustafsson,
eds., Lund (Sweden), 1991, Studentlitteratur, pp.~104 -- 118.

\bibitem{FBrakhagen_TWFogwell_1992a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em {Multigrid Methods
in Modelling Porous Media Flow.}}, in {The Mathematics of Oil Recovery},
P.~R. King, ed., Oxford, 1992, Clarendon Press, pp.~323 -- 336.

\bibitem{JCanu_JLinden_1992a}
{\sc J.~Canu and J.~Linden}, {\em Multigrid solution of {2D Euler} equations:
{\em A Comparison of Osher's and Dick's Flux Difference Splitting Schemes}},
{Arbeitspapiere der GMD} 693, {Gesellschaft f{\"u}r {M}athematik und
{D}atenverarbeitung}, Sankt Augustin, 1992.

\bibitem{JCanu_HRitzdorf_1993a}
{\sc J.~Canu and H.~Ritzdorf}, {\em {Adaptive Block--Structured Multigrid on
Local Memory Machines}}, in Proceedings of the $9^{th}$ GAMM Seminar Kiel on

\bibitem{SRM_de_Barros_1989a}
{\sc S.~R.~M. de~Barros}, {\em {Multigrid methods for two and three dimensional
poisson-type equations on the sphere}}, {Arbeitspapiere der GMD} 391,
{Gesellschaft f{\"u}r {M}athematik und {D}atenverarbeitung}, Sankt Augustin,
1989.

\bibitem{SRM_de_Barros_1991a}
{\sc S.~R.~M. de~Barros}, {\em {Multigrid methods for two and three dimensional
poisson-type equations on the sphere}}, J. Comp. Phys., 92 (1991),
pp.~{313--348}.

\bibitem{SRM_de_Barros_JRBates_FHMSemazzi_RWHiggins_1990b}
{\sc S.~R.~M. de~Barros, J.~R. Bates, F.~H.~M. Semazzi, and R.~W. Higgins},
{\em Integration of the shallow water equations on the sphere using a vector
semi-lagrangian scheme with multigrid solver}, Mon. Wea. Rev., 118 (1990),
pp.~{1615--1627}.

\bibitem{SRM_de_Barros_DPDee_FDickstein_1990a}
{\sc S.~R.~M. de~Barros, D.~P. Dee, and F.~Dickstein}, {\em A multigrid solver
for semi-implicit global shallow-water problems}, Atmos. Ocean, 28 (1990),
pp.~{24--47}.

\bibitem{EDick_JLinden_1989b}
{\sc E.~Dick and J.~Linden}, {\em A multigrid flux-difference splitting method
for steady incompressible {Navier-Stokes} equations}, in Proceedings of 8th
GAMM conference on numerical methods in fluid mechanics, Delft, 1989.

\bibitem{EDick_JLinden_1989a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em A multigrid method
for solving the steady incompressible {Navier-Stokes} equations based on
flux-difference splitting}, in Proceedings of the 6th international
conference on numerical methods in laminar and turbulent flow, Swansea, 1989,
Pineridge Press.

\bibitem{CFrohnSchauf_1992a}
{\sc C.~Frohn-Schauf}, {\em {Flux-Splitting-Methoden und Mehrgitterverfahren
f{\"u}r hyperbolische Systeme mit Beispielen aus der Str{\"o}mungsmechanik}},
PhD thesis, Heinrich-Heine-Universit{\"a}t D{\"u}sseldorf, 1992.

\bibitem{UGaertel_1989a}
{\sc U.~G{\"a}rtel}, {\em {Parallel multigrid solver for 3D anisotropic
problems}}, in Hypercube and Distributed Computers, F.~Andre and J.~Versus,
eds., Amsterdam, 1989, North-Holland.
\newblock Also published as Arbeitspapiere der GMD 390.

\bibitem{UGaertel_MGriebel_WHuber_HSchwichtenberg_1993a}
{\sc U.~G{\"a}rtel, M.~Griebel, W.~Huber, H.~Schwichtenberg, T.~St{\"o}rtkuhl,
U.~Trottenberg, G.~Winter, and C.~Zenger}, {\em The parallel asmg algorithm
for 3d poisson-like equations on multi-workstations}, {Arbeitspapiere der
GMD} 767, {Gesellschaft f{\"u}r {M}athematik und {D}atenverarbeitung}, Sankt
Augustin, 1993.

\bibitem{UGaertel_WJoppich_HRitzdorf_ASchueller_BSteckel_KStueben_1993a}
{\sc U.~G{\"a}rtel, W.~Joppich, H.~Ritzdorf, A.~Sch{\"u}ller, B.~Steckel, and
K.~St{\"u}ben}, {\em {Computational Fluid Dynamics on Parallel Computers --
Two Examples}}, in Proceedings of the Symposium on Affordable Parallel
Processing for Industry and Commerce'', Rutherford Appleton Laboratory, UK,
1993.

\bibitem{UGaertel_WJoppich_ASchueller_HSchwichtenberg_UTrottenberg_GWinter_199%
3a}
{\sc U.~G{\"a}rtel, W.~Joppich, A.~Sch{\"u}ller, H.~Schwichtenberg,
U.~Trottenberg, and G.~Winter}, {\em {Parallel and Cluster Computing on IBM
Systems for Weather Prediction and Related Models: IFS and ASMG}},
{Arbeitspapiere der GMD} 795, {Gesellschaft f{\"u}r {M}athematik und
{D}atenverarbeitung}, Sankt Augustin, 1993.

\bibitem{UGaertel_AKrechel_ANiestegge_HJPlum_1991a}
{\sc U.~G{\"a}rtel, A.~Krechel, A.~Niestegge, and H.-J. Plum}, {\em {Parallel
multigrid for 2D and 3D elliptic equations: standard and nonstandard
smoothing}}, in Multigrid Methods III, W.~Hackbusch and U.~Trottenberg, eds.,
Basel, 1991, Birkh{\"a}user.

\bibitem{UGaertel_KRessel_1991a}
{\sc U.~G{\"a}rtel and K.~Ressel}, {\em {Parallel multigrid: grid partitioning
versus domain decomposition}}, in Computing Methods in Applied Sciences and
Engineering, R.~Glowinski, ed., New York, 1991, Nova Science.
\newblock Also published as Arbeitspapiere der GMD 599.

\bibitem{MHarmatz_PGLauwers_RBenAv_ABrandt_EKatznelson_SSolomon_KWolowesky_199%
1a}
{\sc M.~Harmatz, P.~Lauwers, R.~Ben-Av, A.~Brandt, E.~Katznelson, S.~Solomon,
and K.~Wolowesky}, {\em {Fermion simulations using parallel transported
multigrid}}, in {LATTICE 90, Proceedings of the International Conference on
Lattice Field Theory}, A.~K. U.M.~Heller and S.~Sanielevici, eds.,
Tallahassee, Florida, USA, 1991, North-Holland.

\bibitem{WJoppich_1991b}
{\sc W.~Joppich}, {\em {A Multigrid Algorithm with Time-dependent, Locally
Refined Grids for Solving the Nonlinear Diffusion Equation on a
Nonrectangular Domain}}, in Multigrid Methods III, W.~Hackbusch and
U.~Trottenberg, eds., {Birkh{\"a}user Verlag}, 1991.

\bibitem{WJoppich_SMijalkovic_1993a}
{\sc W.~Joppich and S.~Mijalkovi\'{c}}, {\em Multigrid Methods for Process
Simulation}, Computational Microelectronics, {Springer Verlag Wien, New
York}, 1993.

\bibitem{PGLauwers_1991a}
{\sc P.~Lauwers}, {\em {Multiscale Monte Carlo Algorithms in statistical
mechanics and quantum field theory}}, in {Multigrid Methods III, Proceedings
of the Third European Conference on Multigrid Methods}, W.~Hackbusch and
U.~Trottenberg, eds., Bonn, Germany, 1991, Birkh{\"a}user.

\bibitem{PGLauwers_1993a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em {Multiscale methods
for computing propagators in lattice gauge theory}}, {Arbeitspapiere der GMD}
782, {Gesellschaft f{\"u}r {M}athematik und {D}atenverarbeitung}, Sankt
Augustin, 1993.

\bibitem{MLemke_1993a}
{\sc M.~Lemke}, {\em {Multilevelverfahren mit selbadjungierten
Gitterverfeinerungen f{\"u}r Parallelrechner mit verteiltem Speicher}}, PhD
thesis, Heinrich-Heine-Universit{\"a}t D{\"u}sseldorf, 1993.

\bibitem{JLinden_GLonsdale_HRitzdorf_ASchueller_1992a}
{\sc J.~Linden, G.~Lonsdale, H.~Ritzdorf, and A.~Sch{\"u}ller}, {\em
{Block--Structured Multigrid for the Navier--Stokes Equations: Experiences
and Scalability Questions}}, in {Proceedings of the Conference on Parallel
CFD~'92}, Elsevier, May 18--20 1992.
\newblock Also published as Arbeitspapiere der GMD 683.

\bibitem{JLinden_GLonsdale_HRitzdorf_ASchueller_1992b}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em {Scalability Aspects
of Parallel Multigrid}}, in Proceedings of the BECAUSE Workshop, October
1992.

\bibitem{JLinden_GLonsdale_BSteckel_KStueben_1989a}
{\sc J.~Linden, G.~Lonsdale, B.~Steckel, and K.~St{\"u}ben}, {\em {Multigrid
for the steady-state incompressible Navier-Stokes equations: a survey}}, in
Lecture Notes in Physics, Vol. 323, Springer, 1989.

\bibitem{JLinden_KStueben_1992a}
{\sc J.~Linden and K.~St{\"u}ben}, {\em {Multigrid methods for partial
differential equations -- a short introduction}}, in Proceedings of the 7th
International Nathiagali Summer College on Physics and Contemporary Needs'',
Nathiagali (Pakistan), 1992.

\bibitem{GLonsdale_ASchueller_1991a}
{\sc G.~Lonsdale and A.~Sch{\"u}ller}, {\em {Maintaining multigrid and parallel
efficiency for the Navier-Stokes equations}}, in Parallel Computational Fluid
Dynamics 1991, {Reinsch et al.}, ed., Elsevier, 1991.

\bibitem{GLonsdale_ASchueller_1991b}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em {Parallel and vector
aspects of a multigrid Navier--Stokes solver}}, {Arbeitspapiere der GMD} 550,
{Gesellschaft f{\"u}r {M}athematik und {D}atenverarbeitung}, Sankt Augustin,
1991.

\bibitem{RALorentz_1990a}
{\sc R.~A. Lorentz}, {\em A new conservative discretization of the {Laplacian}
on irregular grids}, {Arbeitspapiere der GMD} 433, {Gesellschaft f{\"u}r
{M}athematik und {D}atenverarbeitung}, Sankt Augustin, 1990.

{\sc R.~A. Lorentz and W.~R. Madych}, {\em Spline wavelets for ordinary
differential equations}, {Arbeitspapiere der GMD} 562, {Gesellschaft f{\"u}r
{M}athematik und {D}atenverarbeitung}, Sankt Augustin, 1991.

\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Wavelets and
generalized box splines}, Applicable Analysis, 44 (1992), pp.~51 -- 76.

\bibitem{YLuh_1993a}
{\sc Y.~Luh}, {\em {A Study on Narrow Stencil Discretizations and Multigrid
Solvers for the Generalized Stokes Equations}}, in Proceedings of the 4th EMG
Conference, Contributions to Multigrid, Amsterdam, 1993, CWI Tract Series.
\newblock To appear.

\bibitem{OMcBryan_UTrottenberg_1989a}
{\sc O.~McBryan and U.~Trottenberg}, {\em {Multigrid Methods on Parallel
Computers}}, {Arbeitspapiere der GMD} 370, {Gesellschaft f{\"u}r {M}athematik
und {D}atenverarbeitung}, Sankt Augustin, 1989.

\bibitem{KDOertel_KStueben_1988a}
{\sc K.-D. Oertel and K.~St{\"u}ben}, {\em {Multigrid with ILU-smoothing:
Systematic tests and improvements}}, in Notes on Numerical Fluid Dynamics,
Vol. 23, Vieweg, Braunschweig, 1988.

\bibitem{CWOosterlee_HRitzdorf_ASchueller_BSteckel_1994b}
{\sc C.~W. Oosterlee, H.~Ritzdorf, A.~Sch{\"u}ller, and B.~Steckel}, {\em
Experience with a parallel multiblock multigrid solution technique for the
{Euler} equations}, in Proceedings of the 10th GAMM Seminar, W.~Hackbusch and
G.~Wittum, eds., Kiel, 1994.
\newblock to appear.

\bibitem{CWOosterlee_HRitzdorf_ASchueller_BSteckel_1994a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Parallel multigrid
results for {Euler} equations using a large number of blocks}, in High
Performance Computing and Networking; Proceedings of the HPCN Europe
Conference, Volume I, W.~Gentzsch and U.~Harms, eds., Munich, Germany, April
1994, Springer--Verlag, Berlin, pp.~145--150.
\newblock Lecture Notes in Computer Science 796.

\bibitem{CWOosterlee_PWesseling_1994a}
{\sc C.~W. Oosterlee and P.~Wesseling}, {\em On the robustness of a multiple
semi-coarsened grid method}, ZAMM,  (1994).
\newblock to appear.

\bibitem{OPaetzold_1989a}
{\sc O.~P{\"a}tzold}, {\em {Experiences in Programming the Brand/Ron
Multi-Level-Algorithm for 2D-Ising Spin Glasses}}, {Arbeitspapiere der GMD}
419, {Gesellschaft f{\"u}r {M}athematik und {D}atenverarbeitung}, Sankt
Augustin, 1989.

\bibitem{HRitzdorf_ASchueller_BSteckel_KStueben_1994a}
{\sc H.~Ritzdorf, A.~Sch{\"u}ller, B.~Steckel, and K.~St{\"u}ben}, {\em
{$L_iSS$ -- An environment for the parallel multigrid solution of partial
differential equations on general 2D domains}}, Parallel Computing,  (1994).
\newblock To appear; also published as Arbeitspapiere der GMD 759.

\bibitem{HRitzdorf_KStueben_1993a}
{\sc H.~Ritzdorf and K.~St{\"u}ben}, {\em {Adaptive multigrid on distributed
memory computers}}, in Proceedings of the 4th European Conference on
Multigrid Methods, Amsterdam, July 1993. Birkh{\"a}user, 1993, pp.~77 -- 95.
\newblock {Also published as Arbeitspapiere der GMD 781}.

\bibitem{ASchueller_1990a}
{\sc A.~Sch{\"u}ller}, {\em {Numerical treatment of the Navier-Stokes
equations}}, in Proceedings of the 5th GAMM-Seminar, Notes on Numerical Fluid
Mechanics. Volume 30, W.Hack\-busch and R.Rannacher, eds., Braunschweig,
1990, Vieweg.

\bibitem{ASchueller_1993a}
\leavevmode\vrule height 2pt depth -1.6pt width 23pt, {\em Multigrid on
parallel computers}.
\newblock {In: W. Joppich and S. Mijalkovic, {\it Multigrid Methods for Process
Simulation}. Series Computational Microelectronics, Springer}, 1993.

\bibitem{HSchwichtenberg_GWinter_1991a}
{\sc H.~Schwichtenberg and G.~Winter}, {\em {Standard Multigrid-Components in a
Classical Drift-Diffusion Model for MOS Devices}}, in {Multigrid Methods:
Special Topics and Applications II}, W.~Hackbusch and U.~Trottenberg, eds.,
{GMD--Studie 189, Gesellschaft f{\"u}r Mathematik und Datenverarbeitung,
Sankt Augustin}, 1991, pp.~319--329.

\bibitem{RStrasser_GNanz_WJoppich_1993}
{\sc R.~Strasser, G.~Nanz, and W.~Joppich}, {\em {Process Simulation for
Nonplanar Structures with the Multigrid Solver $LiSS$}}, in {Proceedings of
the International Conference on Simulation of Semiconductor devices and
Processes, Vol. 5}, S.~Selberherr, H.~Stippel, and E.~Strasser, eds.,
Springer Verlag Wien New York, 1993.

\end{thebibliography}

\end{document}

------------------------------

End of MGNet Digest
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