Exponential basis functions in solution of incompressible fluid problems with moving free surfaces

Zandi, Sayed Mahdi; Boroomand, B.; Soghrati, Soheil

doi:10.1016/j.jcp.2011.09.016

Cited by 37 publications

(27 citation statements)

References 39 publications

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“…More details for the characteristics of pseudo-inverse algorithm can be found in [32] and also in our previous studies on the implementation of pseudo-inverse technique. [27,30] …”

Section: Solution Methodsmentioning

confidence: 99%

“…This leads to the following algebraic equation and then find four Trefftz bases constructed corresponding to each selection. The details of the selection's strategy are described in [25][26][27][28][29][30].…”

Section: Approximate Green's Functionsmentioning

confidence: 99%

“…In the above relation we denote the pseudo-inverse operator by [] + (see [25][26][27][28][29][30] for more details). To give more insight to the results of the proposed method, the variation of the AGF and its relevant FS in a square and triangle plates, for different types of BCs, is shown in Figures 1 and 2, respectively.…”

Section: Approximate Green's Functionsmentioning

confidence: 99%

“…These bases are formed by considering = q i to evaluate β from (43), and evaluating α in terms of = q i. The range of the parameters (q , q ) are considered as q ∈ {±0.01, ± 0.25, ± 0.5, … , ± 5} and q ∈ {±0.01, ± 0.25, ± 0.5, … , ± 5}, (see [25][26][27][28][29][30] for more details on the appropriate selection of α and β).…”

Section: Inverse Single Concentrated Load Identificationmentioning

confidence: 99%

“…The idea of using EBFs, coming from our previous studies in [25][26][27][28][29][30], enables us to solve a wide range of problems with different domain shapes and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions

Movahedian

Boroomand

2015

Inverse Problems in Science and Engineering

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“…More details for the characteristics of pseudo-inverse algorithm can be found in [32] and also in our previous studies on the implementation of pseudo-inverse technique. [27,30] …”

Section: Solution Methodsmentioning

confidence: 99%

Section: Approximate Green's Functionsmentioning

confidence: 99%

Section: Approximate Green's Functionsmentioning

confidence: 99%

Section: Inverse Single Concentrated Load Identificationmentioning

confidence: 99%

“…The idea of using EBFs, coming from our previous studies in [25][26][27][28][29][30], enables us to solve a wide range of problems with different domain shapes and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions

Movahedian

Boroomand

2015

Inverse Problems in Science and Engineering

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Implementation of a generalized exponential basis functions method for linear and non‐linear problems

Mossaiby

Ghaderian

Rossi

2015

Numerical Meth Engineering

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SUMMARYIn this paper, we address shortcomings of the method of exponential basis functions (EBF) by extending it to general linear and non-linear problems. In linear problems, the solution is approximated using a linear combination of exponential functions. The coefficients are calculated such that the homogenous form of equation is satisfied on some grid. To solve non-linear problems, they are converted to into a succession of linear ones using a Newton-Kantorovich approach. While the good characteristics of EBF are preserved, the generalized exponential basis functions method (GEBF) developed can be implemented with greater ease, as all calculations can be performed using real numbers and no characteristic equation is needed. The details of an optimized implementation are described. To study the performance of GEBF, we compare it on some benchmark problems with methods in the literature, such as variants of the boundary element method, where GEBF shows a good performance. Also in a 3D problem, we report the run time of the proposed method compared to Kratos, a parallel, highly optimized finite element code. The results show that to obtain the same level of error in the solution, much less computational effort and degrees of freedom is needed in the proposed method. Practical limits might be found however for large problems because of dense matrix operations involved.

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A Green's discrete transformation meshfree method for simulating transient diffusion problems

Mai

Soghrati

Buchheit

2016

Numerical Meth Engineering

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SUMMARYThis manuscript presents the formulation and application of the Green's discrete transformation method (GDTM) for the meshfree simulation of transient diffusion problems, including those with moving boundaries. The GDTM implements a linear combination of time-dependent Green's basis functions defined on a set of source points to approximate the field in the form of a solution series. A discrete transformation is implemented to evaluate unknown coefficients of this series, which eliminates the need to use time integration schemes. We will study the optimal number and location of the GDTM source points that yield the highest level of accuracy, while maintaining a manageable condition number for the resulting linear system of equations. The optimal values of these parameters, which are inherently independent of the domain geometry, are determined such that the basis functions have appropriate features for approximating the field. A comprehensive convergence study is presented to show the precision and convergence rate of the GDTM for modeling various diffusion problems. We also demonstrate the application of this method for simulating three diffusion problems with complex and evolving morphologies: heat transfer in a turbine blade, thermal response of a porous material, and localized (pitting) corrosion in stainless steel.

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Exponential basis functions in solution of incompressible fluid problems with moving free surfaces

Cited by 37 publications

References 39 publications

Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions

Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions

Implementation of a generalized exponential basis functions method for linear and non‐linear problems

A Green's discrete transformation meshfree method for simulating transient diffusion problems

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