A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants

被引：158

作者：

Huynh, D. B. P. ^{[1
]}

Rozza, G.

Sen, S.

Patera, A. T.

机构：

[1] Natl Univ Singapore, Singapore MIT Alliance, Singapore 117576, Singapore

[2] MIT, Dept Mech Engn, Cambridge, MA 02139 USA

来源：

COMPTES RENDUS MATHEMATIQUE | 2007年 / 345卷 / 08期

关键词：

D O I：

10.1016/j.crma.2007.09.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

posteriori error analysis of reduced basis approximations to affinely parametrized partial differential equations. The method, based on an Offline-Online strategy relevant in the reduced basis many-query and real-time context, reduces the Online calculation to a small Linear Program: the objective is a parametric expansion of the underlying Rayleigh quotient; the constraints reflect stability information at optimally selected parameter points. Numerical results are presented for coercive elasticity and non-coercive acoustics Helmholtz problems.

引用

页码：473 / 478

页数：6

共 10 条

[1] AUTOMATIC CHOICE OF GLOBAL SHAPE FUNCTIONS IN STRUCTURAL-ANALYSIS [J].

ALMROTH, BO ;

STERN, P ;

BROGAN, FA .

AIAA JOURNAL, 1978, 16 (05) :525-528

[2]

Cristescu N.D., 2004, Mechanics of Elastic Composites

[3]

Cuong Nguyen Ngoc, 2005, Handbook of Materials Modeling, P1529

[4]

HUYNH DBP, IN PRESS M3AS

[5]

ISAACSON E, 1994, COMPUTATION EIGENVAL, P61901

[6] A GERSGORIN-TYPE LOWER BOUND FOR THE SMALLEST SINGULAR VALUE [J].

JOHNSON, CR .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 112 :1-7

[7] REDUCED BASIS TECHNIQUE FOR NON-LINEAR ANALYSIS OF STRUCTURES [J].

NOOR, AK ;

PETERS, JM .

AIAA JOURNAL, 1980, 18 (04) :455-462

[8]

PARLETT B. N., 1980, The Symmetric Eigenvalue Problem

[9] Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods [J].

Prud'homme, C ;

Rovas, DV ;

Veroy, K ;

Machiels, L ;

Maday, Y ;

Patera, AT ;

Turinici, G .

JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME, 2002, 124 (01) :70-80

[10] Natural norm a posteriori error estimators for reduced basis approximations [J].

Sen, S. ;

Veroy, K. ;

Huynh, D. B. P. ;

DepariS, S. ;

Nguyen, N. C. ;

Patera, A. T. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 217 (01) :37-62

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