Application of meshfree methods for solving the inverse one-dimensional Stefan problem

Rashedi, Kamal; Adibi, Hojatollah; Rad, Jamal Amani; Parand, Kourosh

doi:10.1016/j.enganabound.2013.10.013

Cited by 27 publications

(11 citation statements)

References 92 publications

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“…Compared to the FEM and the BEM, this type of method is meshless, and the approximate solutions are constructed based on a cluster of scattered nodes [30][31][32][33][34][35][36]. Many meshless methods are derived from a weak-form formulation on global domain or a set of local sub-domains.…”

Section: Introductionmentioning

confidence: 99%

Pricing European and American Options Using a Very Fast and Accurate Scheme: The Meshless Local Petrov–Galerkin Method

Rad

Parand

Abbasbandy

2015

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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In this paper, a method for the numerical pricing of American and European options under the Black-Scholes model is introduced. This approach is meshless local Petrov-Galerkin (MLPG) based on local weak form and the moving least squares approximations. The MLPG offers advantages over conventional and strong meshless methods of radial basis function approximations. In this paper, the American option which is a free boundary problem, is reduced to a fixed boundary problem using a Richardson extrapolation technique. Then a time stepping method is employed for the time derivative. Finally numerical results are presented in two test cases. These experiments show that MLPG approach is accurate and fast, and performs significantly better compared to the conventional radial basis functions collocation methods.

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Section: Introductionmentioning

confidence: 99%

Pricing European and American Options Using a Very Fast and Accurate Scheme: The Meshless Local Petrov–Galerkin Method

Rad

Parand

Abbasbandy

2015

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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“…Большое количество работ посвящено разработке методов численного решения гра-ничных обратных двухфазных задач Стефана [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], связанных с определением гранич-ных условий первого или второго рода или коэффициента теплоотдачи. В [13][14][15][16][17][18][19][20][21][26][27][28] в качестве дополнительной информации задается изменение температуры от времени во внутренних точках исследуемой области и сведения о положении или движении фронта фазового перехода.…”

Section: Introductionunclassified

“…В [13][14][15][16][17][18][19][20][21][26][27][28] в качестве дополнительной информации задается изменение температуры от времени во внутренних точках исследуемой области и сведения о положении или движении фронта фазового перехода. В [22- 25,29] предполагается известной только информация об изме-нении температуры.…”

Section: Introductionunclassified

“…В [26][27][28][29] численное решение поставленных обратных задач выполняется бессеточ-ными методами. При этом обратная задача сводится к системе алгебраических уравнений [26][27][28] или к минимизации целевой функции [29].…”

Section: Introductionunclassified

“…При этом обратная задача сводится к системе алгебраических уравнений [26][27][28] или к минимизации целевой функции [29].…”

Section: Introductionunclassified

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Numerical Solution for an Inverse Problem About Determination of Volumetric Heat Capacity of Rock Mass During Artificial Freezing

2017

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Желнин М.С., Плехов О.А., Семин М.А., Левин Л.Ю. Численное решение обратной задачи определения объемной теплоемкости породного массива в процессе искусственного замораживания // Вестник Пермского национального исследовательского политехнического университета. Механика.

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Efficient numerical methods for boundary data and right‐hand side reconstructions in elliptic partial differential equations

Rashedi

Adibi

Dehghan

2015

Numerical Methods Partial

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In this article, we discuss the application of two important numerical methods, Ritz-Galerkin and Method of Fundamental Solutions (MFS), for solving some inverse problems, arising in the context of two-dimensional elliptic equations. The main incentive for studying the considered problems is their wide applications in engineering fields. In the previous literature, the use of these methods, particularly MFS for right hand side reconstruction has been limited, partly due to stability concerns. We demonstrate that these diculties may be surmounted if the aforementioned methods are combined with techniques such as dual reciprocity method(DRM). Moreover, we incorporate some iterative regularization techniques. This fact is especially veried by taking into account the noisy data with boundary conditions. In addition, parts of this article are dedicated to the problem of boundary data approximation and the issue of numerical stability, ending with a general discussion on the advantages and disadvantages of various methods.

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Application of meshfree methods for solving the inverse one-dimensional Stefan problem

Cited by 27 publications

References 92 publications

Pricing European and American Options Using a Very Fast and Accurate Scheme: The Meshless Local Petrov–Galerkin Method

Pricing European and American Options Using a Very Fast and Accurate Scheme: The Meshless Local Petrov–Galerkin Method

Numerical Solution for an Inverse Problem About Determination of Volumetric Heat Capacity of Rock Mass During Artificial Freezing

Efficient numerical methods for boundary data and right‐hand side reconstructions in elliptic partial differential equations

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