SEMINARIO MATEMATICO Università' e Politecnico Torino

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Aims

The Seminario Matematico is a society of members of various departments concerned with Mathematics in the University and Politechnic of Turin. Its scope is to promote studies and rescarch in ali fields of Mathematics and its applications, and to contribute to the difFusion of mathematica! culture. The Scientifìc Committee of the Seminario Matematico is elected from full professors of Mathematics.

The Rendiconti is the journal of the Seminario Matematico. It publishes papers and invited lectures. Papers should provide originai research contributions. Invited lectures should have a tutorial or overview character.

Instructioiis to Authors

Interested authors should subniit three copies of their papers to the following address:

Seminario Matematico dell'Università e del Politecnico di Torino Via Carlo Alberto 10 10123 Torino (Italy)

The final decision on acceptance of a. paper is ni ad e by the Scientifìc Commit­tee, based upon the evaluations of an extern al referee. Papers must be typewritten, doublc-spaced using A4 format paper ou one side only. Preforred language is En-glish, but Italian and Frcnch may also be submitted. We would prefer authors to prcpare their manuscripts using any version of TjjjX. Corresponding fìles should only be supplied in the case of acceptance. The first page should contain name of author(s) and afhliation(s), title of the paper, a bri.ef abstract and complete mailing address. Authors will receive 50 free reprints of their papers. Orders for larger numbers should be sent together with corrected proofs.

Subscriptions

The Rendiconti is published in volumes of 4 issues per year. One or more issue(s) may be devoted to special topics.

Subscription rates for 1992: Italy, L. 140,000 - Europe, L. 190,000 - Other Countries, L. 265,000.

Prices are quoted in Italian liras, sur face mail postage included. The back years are offered at the current subscription price. Advance payment required. Available on standing order.

Payment: - by postai giro 1157110(5 or intoniational money order - bank transfer (please, add. 5,000) - scnding invoice (institutions only) - charge on credit card (Mastercard, Visa)

Ali Communications concerning subscriptions should be addressed to:

Rosenberg Si Sellier, Editori in Torino Via Andrea Dori a 14 10123 Torino (Italy)

COMMISSIONE SCIENTIFICA Triennio 1987-1990

F. Ricci (Direttore), A. Negro (Vice Direttore), A. Bacciotti, S. Benenti, A. Collino, F. Fava, S. Greco,

G. Monegato, F. Previale, L. Rodino

COMITATO DI REDAZIONE Triennio 1987-1990

E. Abbena, P. Baratella, L. Giacardi, F. Pastrone, G. Rossi

* * *

COMMISSIONE SCIENTIFICA Triennio 1990-1993

S. Benenti (Direttore), A. Bacciotti (Vice Direttore), R. Betti, C. Canuto, F. De Felice, B. Gabutti, C. Massaza,

A. Negro, L. Picco Botta, A. Sanini

COMITATO DI REDAZIONE Triennio 1990-1993

E. Abbena, F. Arzarello, P. Baratella, C.S. Roero, G. Rossi

FASCICOLO SPECIALE 1991

RENDICONTI DEL

SEMINARIO MATEMATICO

NUMERICA!. METHODS

IN APPLIED SCIENCE AND INDUSTRY

UNIVERSITÀ' E POLITECNICO TORINO

Proprietà letteraria riservata

La presente Rivista è parzialmente finanziata dal Consiglio Nazionale delle Ricerche

Direttore responsabile: Fulvio RICCI (1987-1990) Sergio BENENTI (1990-1993)

Autorizzazione del Tribunale di Torino N. 2962 del 6/VI/1980

PRÉFACE

This issue of the "Rendiconti del Seminario Matematico dell'Univer­sità e del Politecnico di Torino" contains the invited papers presented at the "International Conference on Numerical Methods in Applied Science and In-dustry", held at the Politecnico di Torino on June 18-21, 1990. The papers appear according to the order of orai presentation.

The aim of the Conference was to bring together leading scientists in-volved in the development of advanced numerical techniques with actual and potential users working on sophisticated technological applications. Attendees carne from Universities, public research laboratories and industry.

The topics discussed in the papers here collected range from questions of theoretical numerical analysis to applications of numerical algorithms in indu­striai problems. Four papers deal with various aspects of the discretization of boundary integrai equations: extrapolation-based quadrature formulae, spline collocation methods, multigrid techniques and transformation of domain in­tegrate to the boundary. One paper describes recent advances in the coupling of finite element and boundary element methods. Pive contributions are con-cerned with finite element methods: two of them propose efficient techniques Jor solving the related discrete equations, via algebraic multilevel iteraiions or matrix-free implicit time-marching; the three other papers describe applica­tions in elasticity, elasto-plasticity and wave propagation. Finally, two papers discuss the use of numerical methods in the automotive industry.

The Conference was made possible by the contributions from the Italian National Council of Research (C.N.R.), the University and the Politecnico of Torino, the FIAT Research Centre and the Cassa di Risparmio di Torino.

Torino, October 1991 Franco Brezzi Claudio Canuto Luigi Gatteschi Giovanni Monegato

C O N T E N T S

I. BABUSKA - B. ANDERSSON - L. LI - T. von PETERSDORFF - pag. 1 Reliability of finite element analysis

0 . AXELSSON - On algebraic multilevel iteration methods for sei- pag. 31 fadjoint elliptic problems with anisotropy

C.A. BREBBIA - On two difrerent methods for transforming domain pag. 63 integrals to the boundary

A.L. ETEROVIC - K.J. BAT1IE - On large strain elasto-plastic analy- pag. 81 sis with frictional contact conditions

G.C. IISIAO - Some recent developments on the coupling of finite eie- pag. 95 ment and boundary element methods

J.A. TOMAS - S.M. TRINDER - U.C. WILLE - Changing the shape pag. 113 of vehicle components for improved performance

Z. JOHAN - T.J.R. HUGHES - F. SHAKIB - A matrix-free implicit pag. 141 iterative solver for compressible flow problems

W. HACKBUSCH - The solution of large systems of bem equations by pag. 163

the multi-grid and panel clustering technique

J.N. LYNESS - Extrapolation-based boundary element quadrature pag. 189

P.P. STRON A - The role of numerical methods at Fiat Research Center pag. 205

J. DOUGLAS - J.E. SANTOS - J L. HENSLEY - M.E. MORLEY - pag. 223 Simulation of waves arising in acoustic well-logging

S. PROSSDORF - Spline collocation methods for boundary integrai pag. 245 equations in IR"

Finito di stampare nel mese di marzo 1992 presso la M. S./Litografia s.r.l. - Torino

per conto del Seminario Matematico dell'Università e del Politecnico di Torino Via Carlo Alberto, 10 - 10123 TORINO

Special issues and Conference Proceedings published in Rendiconti

Stochastic Problems in Mechanics (1982) Linear Partial and Pseudo-difrerential Operators (1983) DifTerential Geometry on Ifomogeneous Spaces (1983) Special Functions: Tlieory and Computation (1985) Algebraic Varieties of Srnall Dimension (1986) Linear and Nonlinear Mathematical Control Tlieory (1987) Logic, and Computer Sciences: New Trencls and Applications (1987) Nonlinear flyperbolic Equations in Applied Sciences (1988) Partial DifFerential Equations and Geometry (1989) Some Topics in Nonlinear PDE's (1989) Niimcrical Methods in Applied Science and Industry (1991)

Forthcoming:

Mathematical Tlieory of Dynamical Systems and ODE's Commutative Algebra and Algebraic Geometry

Rendiconti del Seminario Università e Politecnico - Torino

FASCICOLO SPECIALE 1991

CONTENTS

I. BABUSKA - B. ANDERSSON - L. LI - t . von PETERSDORFF - pag. 1 Reliability of finite element analysis

O. AXELSSON - On algebraic multilevel iteration methods for sei- pag. 31 fadjoint elliptic problems with anisotropy

C.A. BREBBIA - On two different methods for transforming domain pag. 63 integrals to the boundary

A.L. ETEROVIC - K.J. BATI1E - On large strain elasto-plastic analy- pag. 81 sis with frictional contact condìtions

G.C. IISIAO - Some recent clevelopments on the coupling of finite eie- pag. 95 ment and boundary element methods

J.A. TOMAS - S.M. TRINDER - U.C. WILLE - Changing the shape pag. 113 of vehicle components for irnproved performance

Z. JOIIAN - T.J.R. HUGHES - F. SHAKI!) - A matrix-free implicit pag. 141 iterative solver for compressible flow problems

VV. IIACKIHJSC1I - Tlie solution of large systems of bem equations by pag. 163

the multi-grid and panel clustering technique

J.N. LYNESS - Extrapoiation-based boundary element quadrature pag. 189

P.R STUONA - The iole of numerica! methods at Fiat Research Center pag. 205

J. DOUGLAS - J.E. SANTOS - J.L. HENSLEY - M E . MORLEY - pag. 223 Simulation of waves arising in acoustic well-logging

S. PROSSDORF - Spline collocation methods for boundary integrai pag. 245 equations in IR"

ISSN 0373-1243 EDITRICE UNIVERSITARIA LEVROTTO & BELLA - TORINO