Applied Mathematics and Scientific Computing

by Conference on Applied Mathematics and Scientific Computing (2nd : 2001 : Dubrovnik, Croatia); Drmac, Zlatko; Sopta, Luka

• ISBN13: 9780306474262
• ISBN10: 0306474263
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Plenum Pub Corp

Summary

Proceedings of the second conference on Applied Mathematics and Scientific Computing, held June 4-9, 2001 in Dubrovnik, Croatia. The main idea of the conference was to bring together applied mathematicians both from outside academia, as well as experts from other areas (engineering, applied sciences) whose work involves advanced mathematical techniques. During the meeting there were one complete mini-course, invited presentations, contributed talks and software presentations. A mini-course Schwarz Methods for Partial Differential Equations was given by Prof Marcus Sarkis (Worcester Polytechnic Institute, USA), and invited presentations were given by active researchers from the fields of numerical linear algebra, computational fluid dynamics , matrix theory and mathematical physics (fluid mechanics and elasticity). This volume contains the mini-course and review papers by invited speakers (Part I), as well as selected contributed presentations from the field of analysis, numerical mathematics, and engineering applications.

Table of Contents

Part I Invited lectures
Domain Decomposition Methods	3	(28)
Marcus Sarkis
Introduction	3	(2)
Iterative Methods and Preconditioners	5	(3)
Classical Alternating Schwarz Algorithms	8	(5)
Multidomain Schwarz Methods and Coarse Spaces	13	(2)
Additive Schwarz Methods	15	(1)
Hybrid Schwarz Methods	15	(2)
Abstract Schwarz Theory	17	(7)
Final Remarks	24	(7)
Modification and Maintenance of ULV Decompositions	31	(32)
Jesse L. Barlow
Introduction	31	(3)
Matrix Computational Tools for the ULVD	34	(4)
Forming a ULVD	38	(6)
Modifying a ULVD	44	(12)
Refinining a ULVD	56	(4)
Conclusion	60	(3)
Advances in Jacobi Methods	63	(28)
Zlatko Drmac
Vjeran Hari
Ivan Slapnicar
Two Sided Methods	64	(7)
Asymptotic Convergence	71	(7)
Accuracy	78	(13)
Modelling of curved rods	91	(32)
Mladen Jurak
Josip Tambaca
Zvonimir Tutek
Introduction	91	(1)
Curved rod	92	(2)
Three--dimensional equations of linearized elasticity	94	(3)
Curvilinear coordinates	97	(3)
One--dimensional models of curved rods	100	(7)
The Korn inequality	107	(1)
A priori estimates, convergence	108	(5)
Differential form of curved rod model	113	(3)
Comparison of various curved rod models	116	(7)
Incompressible Newtonian flow through thin pipes	123	(20)
Eduard Marusic-Paloka
Introduction	123	(2)
Poiseuille approximation for pipe with variable cross-section	125	(4)
Justification of the Kirchoff's law	129	(5)
Curved pipes	134	(6)
Conclusion	140	(3)
First Order Eigenvalue Perturbation Theory and the Newton Diagram	143	(36)
Julio Moro
Froilan M. Dopico
Introduction	143	(3)
The Newton Diagram	146	(3)
First order perturbation bounds for eigenvalues	149	(19)
First order perturbation bounds for singular values	168	(3)
First order perturbation bounds for generalized eigenvalues	171	(8)
Part II Contributed lectures
Microlocal energy density for hyperbolic systems	179	(12)
Nenad Antonic
Martin Lazar
Introduction	179	(1)
On H-measures	180	(3)
Main result	183	(4)
Another approach	187	(4)
Approximate solutions to some second order linear recurrences	191	(8)
Katalin Balla
Vilmos Horvat
Introduction	191	(2)
Riccati difference equation for the error term	193	(1)
A simple error estimation	194	(1)
Example	195	(4)
Asymptotic Behaviour of Tension Spline Collocation Matrix	199	(10)
Ivo Beros
Miljenko Marusic
Preliminaries	200	(1)
B-splines	200	(2)
Collocation method	202	(1)
Asymptotic behavior of the collocation matrix	203	(6)
Numerical stability of Krylov subspace iterative methods for solving linear systems	209	(10)
Nela Bosner
Introduction	209	(1)
Iterative methods that recursively compute residual	210	(3)
Methods that solve least squares problem	213	(3)
Conclusion	216	(3)
Nonlinear Problems in Dynamics by the Finite Element in Time Method	219	(10)
Nenad Kranjcevic
Milenko Stegic
Nikola Vrankovic
Introduction	219	(1)
Problem formulation	220	(1)
Finite element in time method	221	(4)
Stability analysis	225	(2)
Concluding remarks	227	(2)
On directional bias of the Lp-norm	229	(8)
Tomislav Marosevic
Introduction	229	(2)
Directional bias of the Lp-norm on R3	231	(2)
Directional bias of the Lp-norm on Rn	233	(4)
A note on slip condition on corrugated boundary	237	(14)
Eduard Marusic-Paloka
Description of the geometry	238	(1)
The equations of motion	239	(1)
Some technical results	240	(1)
Existence, uniqueness, regularity and a priori estimates	241	(3)
The convergence	244	(7)
Relaxation of some energy functionals related to the formation of microstructure	251	(10)
Andrija Raguz
Introduction	251	(1)
Formulation of the problem	252	(2)
Some results	254	(7)
A Coarse Space for Elasticity	261	(14)
Marcus Sarkis
Introduction	261	(1)
Linear Elasticity Discretization	262	(1)
Algebraic Subregions	263	(1)
Overlapping Schwarz Methods	264	(3)
Theoretical Analysis	267	(8)
Numerical Approximations of the Sediment Transport Equations	275	(14)
Luka Sopta
Nelida Crnjaric-Zic
Senka Vukovic
Numerical treatment of the sediment transport equations	277	(1)
Numerical schemes	277	(4)
Exact C-property	281	(2)
Numerical results	283	(3)
Conclusion remarks	286	(3)
A model of irregular curved rods	289	(12)
Josip Tambaca
Introduction	289	(1)
Curved rod model	290	(2)
Curved rod model of irregular rods	292	(3)
Error estimate	295	(2)
Comparison with the junction model	297	(1)
Perspectives	298	(3)
Existence of the density of states for some alloy type models with single site potentials that change sign	301	(12)
Ivan Veselic
Alloy type model and the integrated density of states	301	(2)
Main theorem: A Wegner estimate for indefinite potentials	303	(1)
Sketch of the proof of Theorem 2.1	304	(1)
Discussion and Applications	305	(8)
On principal eigenvalue of stationary diffusion problem with nonsymmetric coefficients	313	(10)
Marko Vrdoljak
Homogenisation of eigenvalue problem	315	(2)
Optimal design for principal eigenvalue optimisation	317	(2)
Singular values	319	(4)
Qualitative Analysis of some Solutions of Quasilinear System of Differential Equations	323	(10)
Bozo Vrdoljak
Alma Omerspahic
Introduction	323	(1)
The main results	324	(6)
Applications	330	(3)
High-Order ENO and WENO Schemes with Flux Gradient and Source Term Balancing	333	(14)
Senka Vukovic
Luka Sopta
Introduction	333	(2)
ENO and WENO Reconstruction via Primitive Function	335	(1)
LLF Formulations	336	(2)
RF Formulations	338	(1)
The One-dimensional Shallow Water Equations and the C-property	339	(2)
Test Problems	341	(2)
Concluding Remarks	343	(4)
Index	347