LEADER 05452nam 2200517 450 001 996490271503316 005 20231110225229.0 010 $a3-031-12616-5 035 $a(CKB)5840000000091739 035 $a(MiAaPQ)EBC7101860 035 $a(Au-PeEL)EBL7101860 035 $a(PPN)264952634 035 $a(EXLCZ)995840000000091739 100 $a20230223d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical methods for mixed finite element problems $eapplications to incompressible materials and contact problems /$fJean Deteix, Thierno Diop and Michel Fortin 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (119 pages) 225 1 $aLecture Notes in Mathematics ;$vv.2318 311 $a3-031-12615-7 320 $aIncludes bibliographical references and index. 327 $aIntro -- Contents -- 1 Introduction -- 2 Mixed Problems -- 2.1 Some Reminders About Mixed Problems -- 2.1.1 The Saddle Point Formulation -- 2.1.2 Existence of a Solution -- 2.1.3 Dual Problem -- 2.1.4 A More General Case: A Regular Perturbation -- 2.1.5 The Case -- 2.2 The Discrete Problem -- 2.2.1 Error Estimates -- 2.2.2 The Matricial Form of the Discrete Problem -- 2.2.3 The Discrete Dual Problem: The Schur Complement -- 2.3 Augmented Lagrangian -- 2.3.1 Augmented or Regularised Lagrangians -- 2.3.2 Discrete Augmented Lagrangian in Matrix Form -- 2.3.3 Augmented Lagrangian and the Condition Number of the Dual Problem -- 2.3.4 Augmented Lagrangian: An Iterated Penalty -- 3 Iterative Solvers for Mixed Problems -- 3.1 Classical Iterative Methods -- 3.1.1 Some General Points -- Linear Algebra and Optimisation -- Norms -- Krylov Subspace -- Preconditioning -- 3.1.2 The Preconditioned Conjugate Gradient Method -- 3.1.3 Constrained Problems: Projected Gradient and Variants -- Equality Constraints: The Projected Gradient Method -- Inequality Constraints -- Positivity Constraints -- Convex Constraints -- 3.1.4 Hierarchical Basis and Multigrid Preconditioning -- 3.1.5 Conjugate Residuals, Minres, Gmres and the Generalised Conjugate Residual Algorithm -- The Generalised Conjugate Residual Method -- The Left Preconditioning -- The Right Preconditioning -- The Gram-Schmidt Algorithm -- GCR for Mixed Problems -- 3.2 Preconditioners for the Mixed Problem -- 3.2.1 Factorisation of the System -- Solving Using the Factorisation -- 3.2.2 Approximate Solvers for the Schur Complement and the Uzawa Algorithm -- The Uzawa Algorithm -- 3.2.3 The General Preconditioned Algorithm -- 3.2.4 Augmented Lagrangian as a Perturbed Problem -- 4 Numerical Results: Cases Where Q= Q -- 4.1 Mixed Laplacian Problem -- 4.1.1 Formulation of the Problem. 327 $a4.1.2 Discrete Problem and Classic Numerical Methods -- The Augmented Lagrangian Formulation -- 4.1.3 A Numerical Example -- 4.2 Application to Incompressible Elasticity -- 4.2.1 Nearly Incompressible Linear Elasticity -- 4.2.2 Neo-Hookean and Mooney-Rivlin Materials -- Mixed Formulation for Mooney-Rivlin Materials -- 4.2.3 Numerical Results for the Linear Elasticity Problem -- 4.2.4 The Mixed-GMP-GCR Method -- Approximate Solver in u -- 4.2.5 The Test Case -- Number of Iterations and Mesh Size -- Comparison of the Preconditioners of Sect.3.2 -- Effect of the Solver in u -- 4.2.6 Large Deformation Problems -- Neo-Hookean Material -- Mooney-Rivlin Material -- 4.3 Navier-Stokes Equations -- 4.3.1 A Direct Iteration: Regularising the Problem -- 4.3.2 A Toy Problem -- 5 Contact Problems: A Case Where Q?Q -- 5.1 Imposing Dirichlet's Condition Through a Multiplier -- 5.1.1 and Its Dual -- 5.1.2 A Steklov-Poincaré operator -- Using This as a Solver -- 5.1.3 Discrete Problems -- The Matrix Form and the Discrete Schur Complement -- 5.1.4 A Discrete Steklov-Poincaré Operator -- 5.1.5 Computational Issues, Approximate Scalar Product -- Simplified Forms of the ps: [/EMC pdfmark [/Subtype /Span /ActualText (script upper S script upper P Subscript h) /StPNE pdfmark [/StBMC pdfmarkSPhps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Operator and Preconditioning -- 5.1.6 The Formulation -- The Choice of h -- 5.1.7 A Toy Model for the Contact Problem -- The Discrete Formulation -- The Active Set Strategy -- 5.2 Sliding Contact -- 5.2.1 The Discrete Contact Problem -- Contact Status -- 5.2.2 The Algorithm for Sliding Contact -- A Newton Method -- The Active Set Strategy -- 5.2.3 A Numerical Example of Contact Problem -- 6 Solving Problems with More Than One Constraint -- 6.1 A Model Problem -- 6.2 Interlaced Method -- 6.3 Preconditioners Based on Factorisation. 327 $a6.3.1 The Sequential Method -- 6.4 An Alternating Procedure -- 7 Conclusion -- Bibliography -- Index. 410 0$aLecture Notes in Mathematics 606 $aFinite element method 606 $aMètode dels elements finits$2thub 608 $aLlibres electrònics$2thub 615 0$aFinite element method. 615 7$aMètode dels elements finits 676 $a620.00151535 700 $aDeteix$b Jean$01258294 702 $aDiop$b Thierno$c(Mathematician), 702 $aFortin$b Michel 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996490271503316 996 $aNumerical methods for mixed finite element problems$93035942 997 $aUNISA LEADER 04257nam 2200589Ia 450 001 9910438099703321 005 20200520144314.0 010 $a9781430257479 010 $a1430257474 024 7 $a10.1007/978-1-4302-5747-9 035 $a(CKB)3710000000015714 035 $a(DE-He213)978-1-4302-5747-9 035 $a(SSID)ssj0000988188 035 $a(PQKBManifestationID)11609045 035 $a(PQKBTitleCode)TC0000988188 035 $a(PQKBWorkID)10951416 035 $a(PQKB)11783635 035 $a(MiAaPQ)EBC1694170 035 $a(CaSebORM)9781430257462 035 $a(PPN)172417201 035 $a(OCoLC)855858049 035 $a(OCoLC)ocn855858049 035 $a(EXLCZ)993710000000015714 100 $a20130716d2013 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLearn Android app development /$fWallace Jackson ; technical reviewer, Michael Thomas 205 $a1st ed. 2013. 210 $aBerkeley, CA $cApress$dc2013 215 $a1 online resource (XXIII, 548 p. 347 illus.) 300 $aIncludes index. 311 08$a9781430257462 311 08$a1430257466 327 $aBuilding an Android IDE for version 4.2 : acquiring, installing, and configuring an Android development environment -- Exploring Android app development : the lingo of Android and building your first hello world app! -- Java for Android primer : enhancing our hello world application -- Layouts and activities : using viewgroup classes -- Android intents and events : adding interactivity -- Android UI design : using views and widgets vis XML -- Android graphics design : concepts and techniques -- Compositing in Android : advanced graphical user interface design -- Android image animation : frame-based animation using XML constructs -- Android vector animation : procedural animation via XML constructs -- An introduction to video : concepts and optimization -- Digital video in Android : using the videoview class -- An introduction to audio : concepts and optimization -- Playing audio in Android : the mediaplayer class -- Audio sequencing : Android soundpool class -- Android intents : inter-application programming -- Android services : using background processing -- Broadcast receivers : Android inter-application communication -- Android content providers : access to datastores -- Building an Android IDE for version 4.12 and earlier : acquiring, installing, and configuring an Android development environment. 330 $aLearn Android App Development is a hands-on tutorial and useful reference. You'll quickly get up to speed and master the Android SDK and the Java that you need for your Android Apps. The Android SDK offers powerful features, and this book is the fastest path to mastering them?and the rest of the Android SDK?for programmers with some experience who are new to Android smartphone and tablet apps development. Many books introduce the Android SDK, but very few explain how to develop apps optimally. This book teaches both core Java language concepts and how to wisely but rapidly employ the design patterns and logic using the Android SDK, which is based on Java APIs. You'll also learn best practices that ensure your code will be efficient and perform well. Get an accelerated but complete enough treatment of the fundamentals of Java necessary to get you started. Design your first app using prototyping and other design methods. Build your first Android app using the code given over the course of the book. Finally, debug and distribute your first app on Google Play or other Android app store. After reading this book, you'll have your first app ready and on the app store, earning you the prestige and the money you seek. 606 $aMobile computing 606 $aApplication software$xDevelopment 615 0$aMobile computing. 615 0$aApplication software$xDevelopment. 676 $a004 700 $aJackson$b Wallace$0709868 701 $aThomas$b Michael$0374372 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438099703321 996 $aLearn Android app development$94186587 997 $aUNINA