Send mail to: mgnet@cs.yale.edu for the digests mgnet-requests@cs.yale.edu for comments or help 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 Additions to mgnet.bib ------------------------------------------------------- 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) Subject: Additions to mgnet.bib 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 entries following your BibTex scheme. 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{RALorentz_WRMadych_1992a} \nocite{RALorentz_WRMadych_1993a} \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 Adaptive Methods, Vieweg, 1993. \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. \bibitem{RALorentz_WRMadych_1993a} {\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. \bibitem{RALorentz_WRMadych_1992a} \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 **************************