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Fast multiscale methods for lattice ...

Martinsson, Per-Gunnar Johan.

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Fast multiscale methods for lattice equations.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fast multiscale methods for lattice equations./
Author:	Martinsson, Per-Gunnar Johan.
Description:	147 p.
Notes:	Source: Dissertation Abstracts International, Volume: 64-07, Section: B, page: 3314.
Contained By:	Dissertation Abstracts International64-07B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3099491

Fast multiscale methods for lattice equations.
Martinsson, Per-Gunnar Johan.

Fast multiscale methods for lattice equations. - 147 p.

Source: Dissertation Abstracts International, Volume: 64-07, Section: B, page: 3314.

Thesis (Ph.D.)--The University of Texas at Austin, 2002.

The thesis concerns multi-scale analysis of equations defined on very large lattices. A new method for model reduction that allows the resolution scale to vary with spatial position is presented. It leads to fast numerical implementations and comes with strict error bounds. This is obtained by incorporating the averaging of the micro-structure directly into a solver that is based on hierarchical data structures, such as the Fast Multipole Method. For boundary value problems, a lattice analogue of the boundary element method is used.Subjects--Topical Terms:

515831
Mathematics.

Fast multiscale methods for lattice equations.
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035 $a (UnM)AAI3099491
035 $a AAI3099491
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100 1 $a Martinsson, Per-Gunnar Johan. $3 1943580
245 1 0 $a Fast multiscale methods for lattice equations.
300 $a 147 p.
500 $a Source: Dissertation Abstracts International, Volume: 64-07, Section: B, page: 3314.
500 $a Supervisors: Ivo Babuska; Gregory J. Rodin.
502 $a Thesis (Ph.D.)--The University of Texas at Austin, 2002.
520 $a The thesis concerns multi-scale analysis of equations defined on very large lattices. A new method for model reduction that allows the resolution scale to vary with spatial position is presented. It leads to fast numerical implementations and comes with strict error bounds. This is obtained by incorporating the averaging of the micro-structure directly into a solver that is based on hierarchical data structures, such as the Fast Multipole Method. For boundary value problems, a lattice analogue of the boundary element method is used.
520 $a Homogenized equations of arbitrary order are derived and strict error bounds are proved. For mechanical lattice structures, special attention is paid to the question of non-degeneracy and whether rotational degrees of freedom should be incorporated. A computer program that automatically derives the homogenized equations was developed. For any lattice geometry, the lattice Green's function is determined and its asymptotic expansion in rational poly-harmonic functions is derived.
520 $a The presented results have applications in many areas of physics and engineering but particular attention is paid to how they can be used to design composite materials with high stiffness-to-weight ratios and prescribed wave-propagation modes. In particular, it is shown how to design materials that have phononic bandgaps, in other words, they block mechanical waves of certain frequencies.
590 $a School code: 0227.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mechanics. $3 1018410
690 $a 0405
690 $a 0346
710 2 0 $a The University of Texas at Austin. $3 718984
773 0 $t Dissertation Abstracts International $g 64-07B.
790 1 0 $a Babuska, Ivo, $e advisor
790 1 0 $a Rodin, Gregory J., $e advisor
790 $a 0227
791 $a Ph.D.
792 $a 2002
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3099491