A greedy meshless local Petrov-Galerkin methodbased on radial basis functions

Mirzaei, Davoud

doi:10.1002/num.22031

Cited by 23 publications

(4 citation statements)

References 24 publications

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“…Incorporating the term of penalty (25) to the high-dimensional Black-Scholes PDE (17), we attain the following parabolic nonlinear PDE on a fixed domain:…”

Section: American Options With Several Assetsmentioning

confidence: 99%

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A greedy algorithm for partition of unity collocation method in pricing American options

Fadaei

Khan

Akgül

2019

Math Methods in App Sciences

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A greedy algorithm in combination with radial basis functions partition of unity collocation (GRBF‐PUC) scheme is used as a locally meshless method for American option pricing. The radial basis function partition of unity method (RBF‐PUM) is a localization technique. Because of having interpolation matrices with large condition numbers, global approximants and some local ones suffer from instability. To overcome this, a greedy algorithm is added to RBF‐PUM. The greedy algorithm furnishes a subset of best nodes among the points X. Such nodes are then used as points of trial in a locally supported RBF approximant for each partition. Using of greedy selected points leads to decreasing the condition number of interpolation matrices and reducing the burdensome in pricing American options.

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“…Incorporating the term of penalty (25) to the high-dimensional Black-Scholes PDE (17), we attain the following parabolic nonlinear PDE on a fixed domain:…”

Section: American Options With Several Assetsmentioning

confidence: 99%

“…Also, this greedy calculated basis is applied for interpolation. In Mirzaei, a local Petrov‐Galerkin method based on greedy algorithm is used. Recently, some meshfree greedy algorithm is used to find a solution of different kinds of PDEs …”

Section: Introductionmentioning

confidence: 99%

A greedy algorithm for partition of unity collocation method in pricing American options

Fadaei

Khan

Akgül

2019

Math Methods in App Sciences

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“…Meshless (or meshfree) approaches are the most important numerical methods for finding the solution of high dimensional (in most cases with complex geometries) differential equations [47] . During last years, meshless approaches provided using the shape functions of moving least squares (MLS) have been extensively applied for divers problems, such as 2D elliptic interface problems [48] , fractional telegraph problem [49] , fractional version of advection-diffusion problem [50] , fractional form of reaction–diffusion equation [51] and integral equations systems [52] .…”

Section: Introductionmentioning

confidence: 99%

SARS-CoV-2 rate of spread in and across tissue, groundwater and soil: A meshless algorithm for the fractional diffusion equation

Bavi

Hosseininia

Heydari

et al. 2022

Engineering Analysis with Boundary Elements

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The epidemiological aspects of the viral dynamic of the SARS-CoV-2 have become increasingly crucial due to major questions and uncertainties around the unaddressed issues of how corpse burial or the disposal of contaminated waste impacts nearby soil and groundwater. Here, a theoretical framework base on a meshless algorithm using the moving least squares (MLS) shape functions is adopted for solving the time-fractional model of the viral diffusion in and across three different environments including water, tissue, and soil. Our computations predict that by considering the (order of fractional derivative) best fit to experimental data, the virus has a traveling distance of in water after 22, regardless of the source of contamination (e.g., from tissue or soil). The outcomes and extrapolations of our study are fundamental for providing valuable benchmarks for future experimentation on this topic and ultimately for the accurate description of viral spread across different environments. In addition to COVID-19 relief efforts, our methodology can be adapted for a wide range of applications such as studying virus ecology and genomic reservoirs in freshwater and marine environments.

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“…The Newton bases for kernel spaces have been introduced in , and the adaptive calculation of them together with a greedy algorithm for interpolation have been presented in . The greedy meshless local Petrov‐Galerkin methods were given in . Finally, a greedy sparse algorithm for linear approximation of functionals has been introduced in .…”

Section: Introductionmentioning

confidence: 99%

Approximate solutions of partial differential equations by some Meshfree Greedy Algorithms

Fadaei

Moghadam

2017

Numerical Methods Partial

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In this article, we use some greedy algorithms to avoid the ill‐conditioning of the final linear system in unsymmetric Kansa collocation method. The greedy schemes have the same background, but we use them in different settings. In the first algorithm, the optimal trial points for interpolation obtained among a huge set of initial points are used for numerical solution of partial differential equations (PDEs). In the second algorithm, based on the Kansa's method, the PDE is discretized to a finite number of test functional equations, and a greedy sparse discretization is applied for approximating the linear functionals. Each functional is stably approximated by some few trial points with an acceptable accuracy. The third greedy algorithm is used to generate the test points. This paper shows that the greedily selection of nodes yields a better conditioning in contrast with usual full meshless methods. Some well‐known PDE examples are solved and compared with the full unsymmetric Kansa's technique. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1884–1899, 2017

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A greedy meshless local Petrov-Galerkin methodbased on radial basis functions

Cited by 23 publications

References 24 publications

A greedy algorithm for partition of unity collocation method in pricing American options

A greedy algorithm for partition of unity collocation method in pricing American options

SARS-CoV-2 rate of spread in and across tissue, groundwater and soil: A meshless algorithm for the fractional diffusion equation

Approximate solutions of partial differential equations by some Meshfree Greedy Algorithms

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