The Decomposition Approach to Inverse Heat Conduction

Lesnic, D.; Elliott, L.

doi:10.1006/jmaa.1998.6243

Cited by 82 publications

(60 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most traditional computational methods including the finite element method and boundary element method for well-posed direct problems fail to produce acceptable solutions to these kinds of inverse problems. Several techniques have been proposed for solving a one-dimensional IHCP [1][2][3][4][5]. Among the methods proposed for higher dimensional IHCP, boundary element [6,7], finite difference [8,9], and finite elements [10,11] have successfully been developed for two-dimensional IHCP and, more recently, the method of fundamental solutions [12] for problems in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Inverse heat conduction problems by using particular solutions

Wen

Hon

2011

Heat Trans. Asian Res.

View full text Add to dashboard Cite

Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two-dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. Least-square and singular value decomposition (SVD) techniques are adopted to solve the ill-conditioned linear system of algebraic equations obtained from the proposed PSRBF method. To demonstrate the effectiveness and simplicity of this approach, several numerical examples are given with satisfactory accuracy and stability.

show abstract

Section: Introductionmentioning

confidence: 99%

Inverse heat conduction problems by using particular solutions

Wen

Hon

2011

Heat Trans. Asian Res.

View full text Add to dashboard Cite

show abstract

“…In 1999, Lesnic and Elliott [30] employed ADM for solving some inverse boundary value problems in heat conduction, also they applied the modification method to deal with noisy input data and obtain a stable approximate solution. In [32] Lesnic investigated the application of the decomposition method involving computational algebra for solving more complicated problems with Dirichlet, Neumann or mixed boundary conditions.…”

Section: Improvement Of the Inverse Operator With Mixed Boundary Condmentioning

confidence: 99%

“…In [32] Lesnic investigated the application of the decomposition method involving computational algebra for solving more complicated problems with Dirichlet, Neumann or mixed boundary conditions. In [30] the authors defined the opera- …”

Section: Improvement Of the Inverse Operator With Mixed Boundary Condmentioning

confidence: 99%

“…We will make an extension to the inverse operator (4.1) given in [30] to all cases of problems, so that we consider in this section, two types of problems:…”

Section: Improvement Of the Inverse Operator With Mixed Boundary Condmentioning

confidence: 99%

“…Adomian [29] suggested a modified method for the hyperbolic, parabolic and elliptic partial differential equations with initial and boundary conditions by using two equations for u, one inverting the t L operator and the other inverting the x L operator, then, adding them and dividing by two. Further, with regards to the mixed value problems, Lesnic and Elliot [30] proposed the inverse operator defined by are known functions. However, in this paper, we will present a modified recursion scheme based on the reliable modification of the ADM with new structure of the inverse operator applied to the (BVPs) with mixed boundary conditions using Lesnic's approach and Ebaid's method.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

Alzaid¹,

Bakodah²

2018

AJCM

View full text Add to dashboard Cite

In this paper, we extend the reliable modification of the Adomian Decomposition Method coupled to the Lesnic's approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.

show abstract

Missing boundary data reconstruction for the heat equation

Abda

Benmeghnia

Guetat

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

This work is concerned with the boundary data completion problem related to the heat equation in the special case of an annular domain. We first reformulate this inverse problem into an interfacial equation involving Steklov‐Poincaré operator based on fictitious domain decomposition techniques. We present some theoretical results. For solving the problem under consideration, we suggest a new numerical point of view which helps to reduce the computational cost using the Schur complement algorithm. We perform then the convergence analysis of this new approach in the annular domain. Several numerical experiments are shown to illustrate the efficiency of the proposed method.

show abstract

The Decomposition Approach to Inverse Heat Conduction

Cited by 82 publications

References 11 publications

Inverse heat conduction problems by using particular solutions

Inverse heat conduction problems by using particular solutions

Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

Missing boundary data reconstruction for the heat equation

Contact Info

Product

Resources

About