Periodic boundary conditions and the error-controlled fast multipole method:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Jülich
Forschungszentrum, Zentralbibliothek
2012
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| Schriftenreihe: | Schriften des Forschungszentrums Jülich
IAS series ; Vol. 11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | V, 126 S. graph. Darst. 24 cm |
| ISBN: | 9783893367702 |
Internformat
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| 100 | 1 | |a Kabadshow, Ivo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Periodic boundary conditions and the error-controlled fast multipole method |c Ivo Kabadshow. Forschungszentrum Jülich GmbH ... |
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 1
L. I. THE IV-BODY PROBLEM I
1.1.1. SIMPLE SCHEMES TO REDUCE THE COMPLEXITY 3
1.1.2. DIFFERENT TYPES O F POTENTIALS 3
1.2. FAST SUMMATION TECHNIQUES 3
2. FMM IN THREE D I M E N S I O N S 7
2.1. INFORMAL DESCRIPTION O F THE F M M 7
2.2. MATHEMATICAL PRELIMINARIES 10
2.2.1. EXPANSION O F THE INVERSE DISTANCE 11
2.2.2. SPHERICAL HARMONIC ADDITION THEOREM 12
2.2.3. EXPANSION O F PARTICLE-PARTICLE INTERACTIONS 15
2.2.4. ADDITION THEOREM FOR REGULAR SOLID HARMONICS 17
2.2.5. ADDITION THEOREM FOR IRREGULAR SOLID HARMONICS 18
2.2.6. FORMAL DOUBLE SUM MANIPULATIONS 19
2.3. MATHEMATICAL OPERATORS 20 *
2.3.1. TRANSLATION O F A MULTIPOLE EXPANSION (M2M) 2 0
2.3.2. CONVERSION O F A MULTIPOLE EXPANSION INTO A LOCAL EXPANSION (M2L)
. . 21 2.3.3. TRANSLATION O F A LOCAL EXPANSION (L2L) 2 2
2.3.4. ROTATION-BASED OPERATORS 2 5
2.3.5. FURTHER OPERATOR COMPRESSION 2 6
2.4. C(./V LOG IV) ALGORITHM 27
2.5. O ( N ) ALGORITHM 3 0
2.6. IMPLEMENTATION DETAILS 35
2.6.1. FRACTIONAL TREE DEPTH 35
2.6.2. DATA STRUCTURES 3 6
2.6.3. MINIMIZATION O F NEAR FIELD AND FAR FIELD COMPUTATION TIME 4 0
2.6.4. LIMITATIONS O F THE ALGORITHM 41
2.7. ERROR ANALYSIS 4 4
2.7.1. WORST CASE ERROR BOUND 4 5
2.7.2. IMPROVED WORKFLOW / ERROR BOUND 4 7
2.7.3. STAGE I O F THE ERROR ESTIMATION SCHEME 4 8
2.7.4. STAGE II O F THE ERROR ESTIMATION SCHEME 54
HTTP://D-NB.INFO/1023367920
IMAGE 2
2.7.5. F M M WITHOUT FAR FIELD CONTRIBUTIONS 67
2.7.6. FURTHER ANALYSIS O F THE ERROR BOUND 6 8
3. FMM A N D PERIODIC B O U N D A R Y C O N D I T I O N S 7 7
3.1. MINIMUM IMAGE CONVENTION 7 7
3.2. DEFINITION O F THE BOUNDARY CONDITION 7 8
3.2.1. THREE DIMENSIONAL PERIODICITY 7 8
3.2.2. TWO DIMENSIONAL PERIODICITY 7 9
3.2.3. ONE DIMENSIONAL PERIODICITY 7 9
3.2.4. PERIODIC POTENTIAL AND ENERGY 7 9
3.3. CONVERGENCE O F LATTICE SUMS 80
3.4. EWALD-BASED SUMMATION SCHEMES 81
3.5. PARAMETER-FREE RENORMALIZATION APPROACH 84
3.5.1. INFORMAL DESCRIPTION 84
3.5.2. MATHEMATICAL OPERATORS 84
3.5.3. LATTICE SUM ALGORITHM 86
3.6. IMPLEMENTATION DETAILS 9 0
3.6.1. ADDITIONAL F M M PASS FOR THE LATTICE OPERATOR 91
3.6.2. MODIFICATIONS O F F M M PASS 1-5 91
3.6.3. FRACTIONAL TREE DEPTH AND PERIODIC BOUNDARY CONDITIONS 9 2
3.6.4. DIPOLE CORRECTION 9 2
3.7. PERIODIC BOUNDARIES AND ERROR CONTROL 9 2
3.7.1. STAGE I O F THE ERROR ESTIMATION SCHEME 9 2
3.7.2. STAGE II O F THE ERROR SCHEME 9 4
4. PERFORMANCE DETAILS O F T H E FMM IMPLEMENTATION 101
4.1. SCALING 101
4.2. PRECISION VERIFICATION 102
4.3. BENCHMARK 105
4.4. ADDITIONAL FEATURES 108
5. C O N C L U S I O N A N D FUTURE DIRECTIONS 111
5.1. CONCLUSION I L L
5.2. FUTURE DIRECTIONS 112
A. A P P E N D I X 1 1 5
BIBLIOGRAPHY 121
|
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| ctrlnum | (OCoLC)812261281 (DE-599)DNB1023367920 |
| dewey-full | 530.144 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.144 |
| dewey-search | 530.144 |
| dewey-sort | 3530.144 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
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| isbn | 9783893367702 |
| language | English |
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| physical | V, 126 S. graph. Darst. 24 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Forschungszentrum, Zentralbibliothek |
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| series | Schriften des Forschungszentrums Jülich |
| series2 | Schriften des Forschungszentrums Jülich : IAS series |
| spelling | Kabadshow, Ivo Verfasser aut Periodic boundary conditions and the error-controlled fast multipole method Ivo Kabadshow. Forschungszentrum Jülich GmbH ... Jülich Forschungszentrum, Zentralbibliothek 2012 V, 126 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Schriften des Forschungszentrums Jülich : IAS series Vol. 11 Zugl.: Wuppertal, Univ., Diss., 2010 (DE-588)4113937-9 Hochschulschrift gnd-content Schriften des Forschungszentrums Jülich IAS series ; Vol. 11 (DE-604)BV035812111 11 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025258925&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kabadshow, Ivo Periodic boundary conditions and the error-controlled fast multipole method Schriften des Forschungszentrums Jülich |
| subject_GND | (DE-588)4113937-9 |
| title | Periodic boundary conditions and the error-controlled fast multipole method |
| title_auth | Periodic boundary conditions and the error-controlled fast multipole method |
| title_exact_search | Periodic boundary conditions and the error-controlled fast multipole method |
| title_full | Periodic boundary conditions and the error-controlled fast multipole method Ivo Kabadshow. Forschungszentrum Jülich GmbH ... |
| title_fullStr | Periodic boundary conditions and the error-controlled fast multipole method Ivo Kabadshow. Forschungszentrum Jülich GmbH ... |
| title_full_unstemmed | Periodic boundary conditions and the error-controlled fast multipole method Ivo Kabadshow. Forschungszentrum Jülich GmbH ... |
| title_short | Periodic boundary conditions and the error-controlled fast multipole method |
| title_sort | periodic boundary conditions and the error controlled fast multipole method |
| topic_facet | Hochschulschrift |
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| volume_link | (DE-604)BV035812111 |
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