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| Description
| - In gravity field studies linear combinations of basis functions are often used to approximate the gravitational potential of the Earth or its disturbing part. The problem is interpreted for the exterior of a sphere or an oblate ellipsoid of revolution. As a rule, spherical or ellipsoidal harmonics are used as basis functions within this concept. The second case is less frequent, but is stimulated by a number of driving impulses. In general its investigation and possibilities for routine implementation are given a considerable attention. As known basis functions like spherical or ellipsoidal harmonics are frequency localized. Alternatively, our aim is to study the use of space localize basis functions. We focus on basis functions generated by means of the reproducing kernel in the respective Hilbert space. The use of the reproducing kernel offers a straightforward way leading to entries in Galekin’s matrix of the linear system for unknown scalar coefficients. In spherical case the problem may be solved relatively easily. Nevertheless our effort aims to approximations in the exterior of the oblate ellipsoid of revolution. We show how the reproducing kernel can be obtained and give its series representation. The fundamental problem, however, is the possibility of practical summation of the series that represents the kernel. This makes the computation of the kernel and especially the set of the entries in Galerkin’s matrix, even by means of high performance facilities, rather demanding. In this paper the reproducing kernel is analyzed, split into parts and various methods and tools, including hypergeometric functions and series, differential and integral calculus are used to represent its structure, so as to enable an effective numerical treatment. In the end the relation to Neumann’s function is discusses.
- In gravity field studies linear combinations of basis functions are often used to approximate the gravitational potential of the Earth or its disturbing part. The problem is interpreted for the exterior of a sphere or an oblate ellipsoid of revolution. As a rule, spherical or ellipsoidal harmonics are used as basis functions within this concept. The second case is less frequent, but is stimulated by a number of driving impulses. In general its investigation and possibilities for routine implementation are given a considerable attention. As known basis functions like spherical or ellipsoidal harmonics are frequency localized. Alternatively, our aim is to study the use of space localize basis functions. We focus on basis functions generated by means of the reproducing kernel in the respective Hilbert space. The use of the reproducing kernel offers a straightforward way leading to entries in Galekin’s matrix of the linear system for unknown scalar coefficients. In spherical case the problem may be solved relatively easily. Nevertheless our effort aims to approximations in the exterior of the oblate ellipsoid of revolution. We show how the reproducing kernel can be obtained and give its series representation. The fundamental problem, however, is the possibility of practical summation of the series that represents the kernel. This makes the computation of the kernel and especially the set of the entries in Galerkin’s matrix, even by means of high performance facilities, rather demanding. In this paper the reproducing kernel is analyzed, split into parts and various methods and tools, including hypergeometric functions and series, differential and integral calculus are used to represent its structure, so as to enable an effective numerical treatment. In the end the relation to Neumann’s function is discusses. (en)
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| Title
| - Reproducing kernel for the exterior of an ellipsoid and its use for generating function bases in gravity field studies
- Reproducing kernel for the exterior of an ellipsoid and its use for generating function bases in gravity field studies (en)
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| skos:prefLabel
| - Reproducing kernel for the exterior of an ellipsoid and its use for generating function bases in gravity field studies
- Reproducing kernel for the exterior of an ellipsoid and its use for generating function bases in gravity field studies (en)
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| skos:notation
| - RIV/00025615:_____/12:#0001836!RIV13-MSM-00025615
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| http://linked.open...avai/predkladatel
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/00025615:_____/12:#0001836
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - Earth’s gravity field; geodetic boundary value problems; Green’s functions; variational methods; reproducing kernels; spherical and ellipsoidal harmonics (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...i/riv/kodPristupu
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...telVyzkumneZpravy
| - European Geoscience Union
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...UplatneniVysledku
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| http://linked.open...iv/tvurceVysledku
| - Holota, Petr
- Nesvadba, Otakar
|
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