Inverse determination of spatially varying material coefficients in solid objects
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George S. Dulikravich
,
Sohail R. Reddy
Abstract
Material properties such as thermal conductivity, magnetic permeability, electric permittivity, modulus of elasticity, Poisson's ratio, thermal expansion coefficient, etc. can vary spatially throughout a given solid object as it is the case in functionally graded materials. Finding this spatial variation is an inverse problem that requires boundary values of the field quantity such as temperature, magnetic field potential or electric field potential and its derivatives normal to the boundaries. In this paper, we solve the direct problem of predicting the spatial distribution of the field variable based on its measured boundary values and on the assumed spatial distribution of the diffusion coefficient using radial basis functions, the finite volume method and the finite element method, whose accuracies are verified against analytical solutions. Minimization of the sum of normalized least-squares differences between the calculated and measured values of the field quantity at the boundaries then leads to the correct parameters in the analytic model for the spatial distribution of the spatially varying material property.
Funding source: CNPq
Award Identifier / Grant number: Science Without Borders
Funding source: PRH/ANP
Funding source: CAPES
Funding source: FAPERJ-Brazil
Funding source: Florida International University Presidential Fellowship
Funding source: US Air Force Office of Scientific Research
Award Identifier / Grant number: FA9550-12-1-0440
Funding source: DOE/NETL
Award Identifier / Grant number: DE-FE0023114
Funding source: FIU Instructional and Research Computing Center
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Preface
- In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)
- An inverse source problem for a damped wave equation with memory
- On the Cauchy problem for semilinear elliptic equations
- A unified approach to convergence rates for ℓ1-regularization and lacking sparsity
- Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives
- Numerical testing in determination of sound speed from a part of boundary by the BC-method
- Inverse determination of spatially varying material coefficients in solid objects
- Determination of the initial condition in parabolic equations from boundary observations
Articles in the same Issue
- Frontmatter
- Preface
- In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)
- An inverse source problem for a damped wave equation with memory
- On the Cauchy problem for semilinear elliptic equations
- A unified approach to convergence rates for ℓ1-regularization and lacking sparsity
- Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives
- Numerical testing in determination of sound speed from a part of boundary by the BC-method
- Inverse determination of spatially varying material coefficients in solid objects
- Determination of the initial condition in parabolic equations from boundary observations
