The method of probabilistic solution for 3D Dirichlet ordinary and generalized harmonic problems in finite domains bounded with one surface

Zakradze, Mamuli; Mamporia, Badri; Kublashvili, Murman; Koblishvili, Nana

doi:10.1016/j.trmi.2018.08.005

Cited by 1 publication

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“…In this section we describe the solution of Problem A * by the MPS. It is known(see e.g., [21,24]), that the probabilistic solution of Problem A * at the fixed point ξ ∈ K R \S R has the following form…”

Section: The Methods Of Probabilistic Solution and Simulation Of The ...mentioning

confidence: 99%

“…In order to simulate the Wiener process we use the following recursion relations (see e.g., [20,24]):…”

Section: The Methods Of Probabilistic Solution and Simulation Of The ...mentioning

confidence: 99%

“…Remark 3. The problems of type A * and B for ellipsoidal, spherical, cylindrical, conic, prismatic, pyramidal and axisymmetric finite domains with a cylindrical hole are considered in [24][25][26][27].…”

Section: The Methods Of Probabilistic Solution and Simulation Of The ...mentioning

confidence: 99%

“…Performed investigations showed (see, e.g., [10,11,[22][23][24][25][26][27]) that the MPS is ideally suited for numerical solution of both classical and generalized (2D and 3D) Dirichlet harmonic problems for a wide class of finite domains only.…”

Section: Introductionmentioning

confidence: 99%

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The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution

et al. 2023

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In the present paper, an algorithm for the numerical solution of the external Dirichlet generalized harmonic problem for a sphere by the method of probabilistic solution (MPS) is given, where “generalized” indicates that a boundary function has a finite number of first kind discontinuity curves. The algorithm consists of the following main stages: (1) the transition from an infinite domain to a finite domain by an inversion; (2) the consideration of a new Dirichlet generalized harmonic problem on the basis of Kelvin’s theorem for the obtained finite domain; (3) the numerical solution of the new problem for the finite domain by the MPS, which in turn is based on a computer simulation of the Weiner process; (4) finding the probabilistic solution of the posed generalized problem at any fixed points of the infinite domain by the solution of the new problem. For illustration, numerical examples are considered and results are presented.

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Section: The Methods Of Probabilistic Solution and Simulation Of The ...mentioning

confidence: 99%

“…In order to simulate the Wiener process we use the following recursion relations (see e.g., [20,24]):…”

Section: The Methods Of Probabilistic Solution and Simulation Of The ...mentioning

confidence: 99%

Section: The Methods Of Probabilistic Solution and Simulation Of The ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution

et al. 2023

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show abstract

The method of probabilistic solution for 3D Dirichlet ordinary and generalized harmonic problems in finite domains bounded with one surface

Cited by 1 publication

References 2 publications

The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution

The Numerical Solution of the External Dirichlet Generalized Harmonic Problem for a Sphere by the Method of Probabilistic Solution

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