Journal ArticleDOI
Detection of material interfaces using a regularized level set method in piezoelectric structures
TLDR
In this paper, an algorithm to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure is proposed, where the material interfaces are implicitly represented by level sets which are identified by applying regularization using total variation penalty terms.Abstract:
An algorithm to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure is proposed. The material interfaces are implicitly represented by level sets which are identified by applying regularization using total variation penalty terms. The inverse problem is solved iteratively and the extended finite element method is used for the analysis of the structure in each iteration. The formulation is presented for three-dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material sub-domains in the presence of higher noise levels.read more
Citations
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Journal ArticleDOI
A level-set based IGA formulation for topology optimization of flexoelectric materials
TL;DR: In this article, a design methodology based on a combination of isogeometric analysis (IGA), level set and point wise density mapping techniques is presented for topology optimization of piezoelectric/flexolectric materials.
Journal ArticleDOI
Phase field modelling of crack propagation, branching and coalescence in rocks
TL;DR: In this paper, a phase field model (PFM) is presented for simulating complex crack patterns including crack propagation, branching and coalescence in rock, based on the strain decomposition for the elastic energy, which drives the evolution of the phase field.
Journal ArticleDOI
Phase field modelling of crack propagation, branching and coalescence in rocks
TL;DR: In this paper, a phase field model (PFM) is presented for simulating complex crack patterns including crack propagation, branching and coalescence in rock, based on the strain decomposition for the elastic energy, which drives the evolution of the phase field.
Journal ArticleDOI
A multi-material level set-based topology optimization of flexoelectric composites
TL;DR: The methodology extends the recently proposed design methodology for a single flexoelectric material and adopts the multi-phase vector level set (LS) model which easily copes with various numbers of phases, efficiently satisfies multiple constraints and intrinsically avoids overlap or vacuum among different phases.
Journal ArticleDOI
Sensitivity and uncertainty analysis for flexoelectric nanostructures
TL;DR: In this article, sensitivity analysis has been applied to identify the key input parameters influencing the energy conversion factor (ECF) of flexoelectric materials, and the sensitivity of the model output to each of the input parameters at different aspect ratios of the beam is quantified by three various common methods, i.e., Morris One-At-a-Time (MOAT), PCE-Sobol', and Extended Fourier amplitude sensitivity test (EFAST).
References
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Journal ArticleDOI
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
Journal ArticleDOI
The partition of unity finite element method: Basic theory and applications
Jens Markus Melenk,Ivo Babuška +1 more
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
Journal ArticleDOI
The use of the L-curve in the regularization of discrete ill-posed problems
TL;DR: A unifying characterization of various regularization methods is given and it is shown that the measurement of “size” is dependent on the particular regularization method chosen, and a new method is proposed for choosing the regularization parameter based on the L-curve.
Algorithms Based on Hamilton-Jacobi Formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: New numerical algorithms, called PSC algorithms, are devised for following fronts propagating with curvature-dependent speed, which approximate Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws.
Book
Computational Methods for Inverse Problems
TL;DR: Inverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting as mentioned in this paper, and a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
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