Inverse shape and surface heat transfer coefficient identification

Lesnic, D.; Bin‐Mohsin, Bandar

doi:10.1016/j.cam.2011.10.020

Cited by 18 publications

(19 citation statements)

References 30 publications

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“…The next task is to reconstruct the source domain Ω 2 numerically. Recently, the MFS has proved, [2,3,19], easy to use in detecting cavities, rigid inclusions, as well as inhomogeneities in inverse geometric problems governed by the modified Helmholtz equation. For a recent review of the MFS, as applied to solving inverse geometric problems, [17].…”

Section: M a T H E M A T I C A L F O R M U L A T I O Nmentioning

confidence: 99%

“…We remark that the normalisation constants usually app earing in the fundamental solution (19) have been omitted, as they were incorporated in the unknown coefficients a and b in (17) and (18), respectively. In the case of the Helmholtz equation when κ ∈ R * + we can avoid using the complex version of the fundamental solution in (19)b yc o n s i d e r i n gi n s t e a do n l y the non-singular part…”

Section: M a T H E M A T I C A L F O R M U L A T I O Nmentioning

confidence: 99%

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Reconstruction of a volumetric source domain

Bin‐Mohsin

Lesnic

2019

JCM

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Inverse and ill-posed problems which consist of reconstructing the unknown support of a three-dimensional volumetric source from a single pair of exterior boundary Cauchy data are investigated. The underlying dependent variable may satisfy the Laplace, Poisson, Helmholtz or modified Helmholtz equations. In the case of a constant physical properties the solutions of these elliptic PDEs are sought asl i n e a rc o m b i n a t i o n so f fundamental solutions, as in the method of fundamental solutions (MFS). The unknown source domain is parametrized by the radial coordinate, as a function of the spherical angles. The resulting least-squares functional estimatingthegapbetweenthemeasured and the computed data is regularized and minimized using the lsqnonlin toolbox routine in Matlab. Numerical results are presented and discussed for both exact and noisy data, confirming the accuracy and stability of reconstruction.

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Section: M a T H E M A T I C A L F O R M U L A T I O Nmentioning

confidence: 99%

Section: M a T H E M A T I C A L F O R M U L A T I O Nmentioning

confidence: 99%

Reconstruction of a volumetric source domain

Bin‐Mohsin

Lesnic

2019

JCM

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“…The method of fundamental solutions is a powerful, accurate, easy to implement and low cost numerical meshless method and has been applied for solving a wide class of stationary and time dependent equations . To present a numerical study, we apply this method for solving IP1–IP3 and investigate its advantages or probable drawbacks in comparison with the Ritz–Galerkin method.…”

Section: Approximation Based On Fundamental Solutionsmentioning

confidence: 99%

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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“…(9)- (13). For this purpose, perturbing f(ϕ) to f(ϕ) + Δf(ϕ), then change θ(η, ϕ) and f(ϕ) to θ(η, ϕ) + Δθ(η, ϕ) and f(ϕ) + Δf(ϕ), respectively.…”

Section: Sensitivity Problemmentioning

confidence: 99%

“…In the heat transfer area, external inverse problems include estimation of temperature, heat flux, or heat transfer coefficient [5,6], and internal inverse problems include determination of thermophysical properties, such as thermal conductivity and heat capacity [7,8]. In addition, the inverse analysis has also been applied to the problems related to shape design [9][10][11] and shape identification [12][13][14].…”

Section: Introductionmentioning

confidence: 99%