. . "RIV/00025615:_____/14:#0002087" . . . "Laplacian and Topography in the Iterative Solution of the Boundary Value Problem of Physical Geodesy"@en . . . . "Vztah mezi popisem fyzick\u00E9ho povrchu Zem\u011B a strukturou Laplaceova oper\u00E1toru nab\u00EDz\u00ED zaj\u00EDmav\u00FD pohled na \u0159e\u0161en\u00ED okrajov\u00FDch probl\u00E9m\u016F teorie potenci\u00E1lu ve fyzik\u00E1ln\u00ED geod\u00E9zii. Podobn\u011B jako v jin\u00FDch oblastech techniky a matematick\u00E9 fyziky tak\u00E9 zde m\u016F\u017Ee b\u00FDti vyu\u017Eita transformace sou\u0159adnic k posouzen\u00ED a volb\u011B alternativy mezi slo\u017Eitost\u00ED hranice a slo\u017Eitost\u00ED koeficient\u016F parci\u00E1ln\u00ED diferenci\u00E1ln\u00ED rovnice, kterou mus\u00ED spl\u0148ovat hledan\u00E9 \u0159e\u0161en\u00ED studovan\u00E9ho probl\u00E9mu, v dan\u00E9m p\u0159\u00EDpad\u011B poruchov\u00FD potenci\u00E1l. Laplace\u016Fv oper\u00E1tor m\u00E1 pom\u011Brn\u011B jednoduchou strukturu pokud je vyj\u00E1d\u0159en ve sf\u00E9rick\u00FDch sou\u0159adnic\u00EDch, kter\u00E9 se \u010Dasto po\u017E\u00EDvaj\u00ED v geod\u00E9zii. Fyzick\u00FD povrch Zem\u011B se v\u0161ak podstatn\u011B li\u0161\u00ED od (geocentrick\u00E9) sf\u00E9ry, by\u0165 s optim\u00E1ln\u011B volen\u00FDm polom\u011Brem, kter\u00E1 reprezentuje jednu ze sou\u0159adnicov\u00FDch ploch v syst\u00E9mu sf\u00E9rick\u00FDch sou\u0159adnic. Situace m\u016F\u017Ee ale b\u00FDti v\u00FDhodn\u011Bj\u0161\u00ED v syst\u00E9mu obecn\u00FDch k\u0159ivo\u010Dar\u00FDch sou\u0159adnic, a to takov\u00FDch, \u017Ee fyzick\u00FD povrch Zem\u011B je vno\u0159en do syst\u00E9mu sou\u0159adnicov\u00FDch ploch. Na druh\u00E9 stran\u011B je v\u0161ak struktura Laplaceova oper\u00E1toru p\u0159i t\u00E9to volb\u011B slo\u017Eit\u011Bj\u0161\u00ED a ve sv\u00E9 podstat\u011B reprezentuje topografii fyzick\u00E9ho povrchu Zem\u011B. V navrhovan\u00E9m postupu jsou vlivy p\u016Fsoben\u00E9 topografi\u00ED zemsk\u00E9ho povrchu interpretov\u00E1ny jako poruchy a \u0159e\u0161en\u00ED studovan\u00E9ho probl\u00E9mu fyzik\u00E1ln\u00ED geod\u00E9zie je zdokonalov\u00E1no v itera\u010Dn\u00EDch kroc\u00EDch konstruovan\u00FDch pomoc\u00ED metody postupn\u00FDch aproximac\u00ED. V r\u00E1mci tohoto konceptu lze pou\u017E\u00EDt sf\u00E9rick\u00FD matematick\u00FD apar\u00E1t v ka\u017Ed\u00E9m itera\u010Dn\u00EDm kroku a pro \u0159e\u0161en\u00FD probl\u00E9m je tak\u00E9 zkonstruov\u00E1na Greenova funkce. Diskutov\u00E1na je rovn\u011B\u017E konvergence itera\u010Dn\u00EDho prostupu a mo\u017En\u00E1 analogie \u0159e\u0161en\u00ED op\u0159en\u00E1 o vyu\u017Eit\u00ED matematick\u00E9ho apar\u00E1tu v\u00E1zan\u00E9ho k zplo\u0161t\u011Bl\u00E9mu rota\u010Dn\u00EDmu elipsoidu." . . . . . "RIV/00025615:_____/14:#0002087!RIV15-GA0-00025615" . . "Laplaci\u00E1n a topografie p\u0159i itera\u010Dn\u00EDm \u0159e\u0161en\u00ED okrajov\u00E9 \u00FAlohy fyzik\u00E1ln\u00ED geod\u00E9zie" . "A relation between the description of the physical surface of the Earth and the structure of the Laplace operator seems to be an important moment in the solution of boundary value problems in physical geodesy. Here, similarly as in other branches of engineering and mathematical physics a transformation of coordinates may be used to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. In a sense, in the theory of the figure of the Earth the problem is of an intrinsic nature. For instance the Laplace operator has a relatively simple structure in terms of spherical coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from a (geocentric) sphere of (even optimally chosen) radius. The situation may be more convenient in a system of curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. However, the structure of the Laplace operator is more complicated and in a sense it represents the topography of the physical surface of the Earth. In the suggested approach the effects caused by the topography of the physical surface of the Earth are interpreted as perturbations and the boundary value problem considered is solved by means of successive approximations. A spherical mathematical apparatus is used in each iteration step. This also enables an easy construction of the respective Green\u2019s function. The convergence of the iterations is discussed as well as the possibility to use a mathematical apparatus related to an oblate ellipsoid of revolution for the solution of the problem."@en . "Vztah mezi popisem fyzick\u00E9ho povrchu Zem\u011B a strukturou Laplaceova oper\u00E1toru nab\u00EDz\u00ED zaj\u00EDmav\u00FD pohled na \u0159e\u0161en\u00ED okrajov\u00FDch probl\u00E9m\u016F teorie potenci\u00E1lu ve fyzik\u00E1ln\u00ED geod\u00E9zii. Podobn\u011B jako v jin\u00FDch oblastech techniky a matematick\u00E9 fyziky tak\u00E9 zde m\u016F\u017Ee b\u00FDti vyu\u017Eita transformace sou\u0159adnic k posouzen\u00ED a volb\u011B alternativy mezi slo\u017Eitost\u00ED hranice a slo\u017Eitost\u00ED koeficient\u016F parci\u00E1ln\u00ED diferenci\u00E1ln\u00ED rovnice, kterou mus\u00ED spl\u0148ovat hledan\u00E9 \u0159e\u0161en\u00ED studovan\u00E9ho probl\u00E9mu, v dan\u00E9m p\u0159\u00EDpad\u011B poruchov\u00FD potenci\u00E1l. Laplace\u016Fv oper\u00E1tor m\u00E1 pom\u011Brn\u011B jednoduchou strukturu pokud je vyj\u00E1d\u0159en ve sf\u00E9rick\u00FDch sou\u0159adnic\u00EDch, kter\u00E9 se \u010Dasto po\u017E\u00EDvaj\u00ED v geod\u00E9zii. Fyzick\u00FD povrch Zem\u011B se v\u0161ak podstatn\u011B li\u0161\u00ED od (geocentrick\u00E9) sf\u00E9ry, by\u0165 s optim\u00E1ln\u011B volen\u00FDm polom\u011Brem, kter\u00E1 reprezentuje jednu ze sou\u0159adnicov\u00FDch ploch v syst\u00E9mu sf\u00E9rick\u00FDch sou\u0159adnic. Situace m\u016F\u017Ee ale b\u00FDti v\u00FDhodn\u011Bj\u0161\u00ED v syst\u00E9mu obecn\u00FDch k\u0159ivo\u010Dar\u00FDch sou\u0159adnic, a to takov\u00FDch, \u017Ee fyzick\u00FD povrch Zem\u011B je vno\u0159en do syst\u00E9mu sou\u0159adnicov\u00FDch ploch. Na druh\u00E9 stran\u011B je v\u0161ak struktura Laplaceova oper\u00E1toru p\u0159i t\u00E9to volb\u011B slo\u017Eit\u011Bj\u0161\u00ED a ve sv\u00E9 podstat\u011B reprezentuje topografii fyzick\u00E9ho povrchu Zem\u011B. V navrhovan\u00E9m postupu jsou vlivy p\u016Fsoben\u00E9 topografi\u00ED zemsk\u00E9ho povrchu interpretov\u00E1ny jako poruchy a \u0159e\u0161en\u00ED studovan\u00E9ho probl\u00E9mu fyzik\u00E1ln\u00ED geod\u00E9zie je zdokonalov\u00E1no v itera\u010Dn\u00EDch kroc\u00EDch konstruovan\u00FDch pomoc\u00ED metody postupn\u00FDch aproximac\u00ED. V r\u00E1mci tohoto konceptu lze pou\u017E\u00EDt sf\u00E9rick\u00FD matematick\u00FD apar\u00E1t v ka\u017Ed\u00E9m itera\u010Dn\u00EDm kroku a pro \u0159e\u0161en\u00FD probl\u00E9m je tak\u00E9 zkonstruov\u00E1na Greenova funkce. Diskutov\u00E1na je rovn\u011B\u017E konvergence itera\u010Dn\u00EDho prostupu a mo\u017En\u00E1 analogie \u0159e\u0161en\u00ED op\u0159en\u00E1 o vyu\u017Eit\u00ED matematick\u00E9ho apar\u00E1tu v\u00E1zan\u00E9ho k zplo\u0161t\u011Bl\u00E9mu rota\u010Dn\u00EDmu elipsoidu."@cs . "1"^^ . "1"^^ . "25648" . . "Z\u00E1mek Kozel" . . "Laplacian and Topography in the Iterative Solution of the Boundary Value Problem of Physical Geodesy"@en . . "Odd\u011Blen\u00ED geomatiky Fakulty aplikovan\u00FDch v\u011Bd Z\u00E1pado\u010Desk\u00E9 univeryity" . . "[ECF88906B791]" . . . "P(ED1.1.00/02.0090), P(GA14-34595S)" . "linear gravimetric boundary value problem; transformation of coordinates; general structure of the Laplace operator; integral representation of the solution; Neumann\u2019s function; method of successive approximations"@en . "Laplaci\u00E1n a topografie p\u0159i itera\u010Dn\u00EDm \u0159e\u0161en\u00ED okrajov\u00E9 \u00FAlohy fyzik\u00E1ln\u00ED geod\u00E9zie"@cs . "Laplaci\u00E1n a topografie p\u0159i itera\u010Dn\u00EDm \u0159e\u0161en\u00ED okrajov\u00E9 \u00FAlohy fyzik\u00E1ln\u00ED geod\u00E9zie" . . . "Holota, Petr" . "Laplaci\u00E1n a topografie p\u0159i itera\u010Dn\u00EDm \u0159e\u0161en\u00ED okrajov\u00E9 \u00FAlohy fyzik\u00E1ln\u00ED geod\u00E9zie"@cs .