Automated hybrid singularity superposition and anchored grid pattern BEM algorithm for the solution of inverse geometric problems

Ni, Marcus; Kassab, Alain J.; Divo, Eduardo

doi:10.1016/j.enganabound.2016.09.004

Cited by 7 publications

(2 citation statements)

References 11 publications

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“…zero Neumann condition) inner boundary from a single set of Cauchy data available on the outer boundary of a domain occupied by an isotropic heat conductive solid using a regularised collocation Trefftz method. A method for solving an inverse geometric problem in steady-state isotropic heat conduction was proposed by Ni et al [20] for the reconstruction of the unknown subsurface cavity geometry using the BEM and a GA, in conjunction with the Nelder-Mead non-linear simplex optimisation method. A numerical procedure based on the Trefftz method that allows, in the framework of stationary isotropic heat conduction, for the reconstruction of an unknown part of a regular domain boundary from the given temperature measurements on it, provided that both the temperature and heat flux on the remaining part of the boundary are known, was proposed by Hozejowski [9].…”

Section: Introductionmentioning

confidence: 99%

Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction

Marin,

Pantea

2024

Numer Algor

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We study the reconstruction of an unknown/inaccesible smooth inner boundary from the knowledge of the Dirichlet condition (temperature) on the entire boundary of a doubly connected domain occupied by a two-dimensional homogeneous anisotropic solid and an additional Neumann condition (normal heat flux) on the known, accessible, and smooth outer boundary in the framework of steady-state heat conduction with heat sources. This inverse geometric problem is approached through an operator that maps an admissible inner boundary belonging to the space of 2π−periodic and twice continuously differentiable functions into the Neumann data on the outer boundary which is assumed to be continuous. We prove that this operator is differentiable and hence a gradient-based method that employs the anisotropic single layer representation of the solution to an appropriate Dirichlet problem for the two-dimensional anisotropic heat conduction, is developed for approximating the unknown inner boundary. Numerical results are presented for both exact and perturbed Neumann data on the outer boundary and show the convergence, stability, and robustness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction

Marin,

Pantea

2024

Numer Algor

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“…Bueno et al (2017) presented a formulation that achieves high levels of accuracy and efficiency by properly solving the Poisson equations at each step of the solution process by formulating a localized RBF collocation meshless method solution approach for the approximation of the diffusive and convective derivatives while using the same framework to implement a dual-reciprocity boundary element method (BEM) for the solution of the ensuing Poisson equations. The BEM and a genetic algorithm are developed in Ni et al (2016) for solving an inverse geometric problem by reconstructing the unknown subsurface cavity geometry. The main aim of Harris et al (2015) is to demonstrate the use of RBF interpolation in the approximation of sharp gradients or shocks by use of a RBF blending interpolation approach.…”

Section: Introductionmentioning

confidence: 99%

Simulation of predator–prey system with two-species, two chemicals and an additional chemotactic influence via direct meshless local Petrov–Galerkin method

Abbaszadeh

Salec

Alwan

2023

HFF

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Purpose This paper aims to introduce a new numerical approach based on the local weak form and the Petrov–Galerkin idea to numerically simulation of a predator–prey system with two-species, two chemicals and an additional chemotactic influence. Design/methodology/approach In the first proceeding, the space derivatives are discretized by using the direct meshless local Petrov–Galerkin method. This generates a nonlinear algebraic system of equations. The mentioned system is solved by using the Broyden’s method which this technique is not related to compute the Jacobian matrix. Findings This current work tries to bring forward a trustworthy and flexible numerical algorithm to simulate the system of predator–prey on the nonrectangular geometries. Originality/value The proposed numerical results confirm that the numerical procedure has acceptable results for the system of partial differential equations.

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Constitutive relation error formalism applied to the solution of inverse problems using the BEM

Oliveira

Leonel

2019

Engineering Analysis with Boundary Elements

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Automated hybrid singularity superposition and anchored grid pattern BEM algorithm for the solution of inverse geometric problems

Cited by 7 publications

References 11 publications

Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction

Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction

Simulation of predator–prey system with two-species, two chemicals and an additional chemotactic influence via direct meshless local Petrov–Galerkin method

Constitutive relation error formalism applied to the solution of inverse problems using the BEM

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