On the Fast Multipole Method for Computing the Energy of Periodic Assemblies of Charged and Dipolar Particles
In two dimensions, it is convenient to represent the coordinates (x, y) of particles as complex numbers z = x + iy. The energy of interaction of two point charges q[sub 1] and q [sub 2] at points represented by the complex numbers z[sub 1] and z[sub 2] is then since the natural logarithm is the sing...
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| Veröffentlicht in: | Journal of computational physics 1993-08, Vol.107 (2), p.403-405 |
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| container_title | Journal of computational physics |
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| creator | Christiansen, Dorthe Perram, John W. Petersen, Henrik G. |
| description | In two dimensions, it is convenient to represent the coordinates (x, y) of particles as complex numbers z = x + iy. The energy of interaction of two point charges q[sub 1] and q [sub 2] at points represented by the complex numbers z[sub 1] and z[sub 2] is then since the natural logarithm is the singular part of the Greens function for the two-dimensional Laplace equation. In performing molecular dynamics and Monte Carlo simulations of neutral systems of charged particles or of point dipoles, it is necessary to compute the energies and forces of an infinite periodic system in which the N charges or dipoles at the points z[sub 1] ... z[sub n] resident in the primary (usually square) simulation cell are replicated everywhere in the plane. |
| doi_str_mv | 10.1006/jcph.1993.1154 |
| format | Article |
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The energy of interaction of two point charges q[sub 1] and q [sub 2] at points represented by the complex numbers z[sub 1] and z[sub 2] is then since the natural logarithm is the singular part of the Greens function for the two-dimensional Laplace equation. In performing molecular dynamics and Monte Carlo simulations of neutral systems of charged particles or of point dipoles, it is necessary to compute the energies and forces of an infinite periodic system in which the N charges or dipoles at the points z[sub 1] ... z[sub n] resident in the primary (usually square) simulation cell are replicated everywhere in the plane.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1006/jcph.1993.1154</identifier><language>eng</language><publisher>Amsterdam: Elsevier Inc</publisher><subject>990200 -- Mathematics & Computers ; Algorithms for functional approximation ; Applied classical electromagnetism ; CALCULATION METHODS ; CHARGED PARTICLES ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; Computational techniques ; COMPUTERIZED SIMULATION ; DIFFERENTIAL EQUATIONS ; Electromagnetism; electron and ion optics ; Electrostatics. 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The energy of interaction of two point charges q[sub 1] and q [sub 2] at points represented by the complex numbers z[sub 1] and z[sub 2] is then since the natural logarithm is the singular part of the Greens function for the two-dimensional Laplace equation. In performing molecular dynamics and Monte Carlo simulations of neutral systems of charged particles or of point dipoles, it is necessary to compute the energies and forces of an infinite periodic system in which the N charges or dipoles at the points z[sub 1] ... z[sub n] resident in the primary (usually square) simulation cell are replicated everywhere in the plane.</description><subject>990200 -- Mathematics & Computers</subject><subject>Algorithms for functional approximation</subject><subject>Applied classical electromagnetism</subject><subject>CALCULATION METHODS</subject><subject>CHARGED PARTICLES</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>Computational techniques</subject><subject>COMPUTERIZED SIMULATION</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>Electromagnetism; electron and ion optics</subject><subject>Electrostatics. Poisson and laplace equations, boundary-value problems</subject><subject>EQUATIONS</subject><subject>Exact sciences and technology</subject><subject>FUNCTIONS</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE</subject><subject>GREEN FUNCTION</subject><subject>ITERATIVE METHODS</subject><subject>LAPLACE EQUATION</subject><subject>Mathematical methods in physics</subject><subject>Molecular dynamics and particle methods</subject><subject>MONTE CARLO METHOD</subject><subject>Numerical approximation and analysis</subject><subject>NUMERICAL SOLUTION</subject><subject>PARTIAL DIFFERENTIAL EQUATIONS</subject><subject>Physics</subject><subject>SIMULATION 661300 -- Other Aspects of Physical Science-- (1992-)</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1993</creationdate><recordtype>article</recordtype><recordid>eNp1kLtPwzAQhy0EEuWxMluINcUXu0k8olIeUisYYI7c86UxSuPIdpH472koYmM66fT97vExdgViCkIUtx84tFPQWk4BZuqITUBokeUlFMdsIkQOmdYaTtlZjB9CiGqmqgnbvvQ8tcQfTEx8teuSG3xHfEWp9ZY3PvC53w675PrND7foKWy-uG_4KwXnrUN-FyNt152jOLbnrQkbstz0lt-Pw0zgryYkhx3FC3bSmC7S5W89Z-8Pi7f5U7Z8eXye3y0zlCpPWW6NqipJSFJbU4IolbZNKTVUSKUu1LosVL4GylGKtVLlLLeiQWlBiUJqlOfs-jDXx-TqiC4Rtuj7njDVs0LKEmAPTQ8QBh9joKYegtua8FWDqEej9Wi0Ho3Wo9F94OYQGExE0zXB9OjiX0rBj9Q9Vh0w2n_46SiMB1CPZF0Y91vv_tvwDU-uiRE</recordid><startdate>19930801</startdate><enddate>19930801</enddate><creator>Christiansen, Dorthe</creator><creator>Perram, John W.</creator><creator>Petersen, Henrik G.</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>19930801</creationdate><title>On the Fast Multipole Method for Computing the Energy of Periodic Assemblies of Charged and Dipolar Particles</title><author>Christiansen, Dorthe ; Perram, John W. ; Petersen, Henrik G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c342t-2da4883ece39da710749df73918ce7964b7642b1e2c30b44752d0fc3d140639c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1993</creationdate><topic>990200 -- Mathematics & Computers</topic><topic>Algorithms for functional approximation</topic><topic>Applied classical electromagnetism</topic><topic>CALCULATION METHODS</topic><topic>CHARGED PARTICLES</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>Computational techniques</topic><topic>COMPUTERIZED SIMULATION</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>Electromagnetism; electron and ion optics</topic><topic>Electrostatics. Poisson and laplace equations, boundary-value problems</topic><topic>EQUATIONS</topic><topic>Exact sciences and technology</topic><topic>FUNCTIONS</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE</topic><topic>GREEN FUNCTION</topic><topic>ITERATIVE METHODS</topic><topic>LAPLACE EQUATION</topic><topic>Mathematical methods in physics</topic><topic>Molecular dynamics and particle methods</topic><topic>MONTE CARLO METHOD</topic><topic>Numerical approximation and analysis</topic><topic>NUMERICAL SOLUTION</topic><topic>PARTIAL DIFFERENTIAL EQUATIONS</topic><topic>Physics</topic><topic>SIMULATION 661300 -- Other Aspects of Physical Science-- (1992-)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Christiansen, Dorthe</creatorcontrib><creatorcontrib>Perram, John W.</creatorcontrib><creatorcontrib>Petersen, Henrik G.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Christiansen, Dorthe</au><au>Perram, John W.</au><au>Petersen, Henrik G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Fast Multipole Method for Computing the Energy of Periodic Assemblies of Charged and Dipolar Particles</atitle><jtitle>Journal of computational physics</jtitle><date>1993-08-01</date><risdate>1993</risdate><volume>107</volume><issue>2</issue><spage>403</spage><epage>405</epage><pages>403-405</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>In two dimensions, it is convenient to represent the coordinates (x, y) of particles as complex numbers z = x + iy. The energy of interaction of two point charges q[sub 1] and q [sub 2] at points represented by the complex numbers z[sub 1] and z[sub 2] is then since the natural logarithm is the singular part of the Greens function for the two-dimensional Laplace equation. In performing molecular dynamics and Monte Carlo simulations of neutral systems of charged particles or of point dipoles, it is necessary to compute the energies and forces of an infinite periodic system in which the N charges or dipoles at the points z[sub 1] ... z[sub n] resident in the primary (usually square) simulation cell are replicated everywhere in the plane.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1006/jcph.1993.1154</doi><tpages>3</tpages></addata></record> |
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| identifier | ISSN: 0021-9991 |
| ispartof | Journal of computational physics, 1993-08, Vol.107 (2), p.403-405 |
| issn | 0021-9991 1090-2716 |
| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | 990200 -- Mathematics & Computers Algorithms for functional approximation Applied classical electromagnetism CALCULATION METHODS CHARGED PARTICLES CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Computational techniques COMPUTERIZED SIMULATION DIFFERENTIAL EQUATIONS Electromagnetism electron and ion optics Electrostatics. Poisson and laplace equations, boundary-value problems EQUATIONS Exact sciences and technology FUNCTIONS Fundamental areas of phenomenology (including applications) GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE GREEN FUNCTION ITERATIVE METHODS LAPLACE EQUATION Mathematical methods in physics Molecular dynamics and particle methods MONTE CARLO METHOD Numerical approximation and analysis NUMERICAL SOLUTION PARTIAL DIFFERENTIAL EQUATIONS Physics SIMULATION 661300 -- Other Aspects of Physical Science-- (1992-) |
| title | On the Fast Multipole Method for Computing the Energy of Periodic Assemblies of Charged and Dipolar Particles |
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