The spectral cell method for wave propagation in heterogeneous materials simulated on multiple GPUs and CPUs

Mossaiby, Farshid; Joulaian, Meysam; Düster, Alexander

doi:10.1007/s00466-018-1623-4

Cited by 16 publications

(5 citation statements)

References 40 publications

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“…For smooth problems, the FCM exhibits high convergence rates and hence, can compete with the p-FEM [28,71]. The FCM is used in a wide range of application-including geometric nonlinearities [81], hyperelasticity and elastoplasticity at small and finite strains [32][33][34][35]53], structural dynamics [9,23,51,69,76], acoustics [73,77], fracture mechanics [47,70], biomechanics [27,31], homogenization [29,40,60], and Isogeometric Analysis (IGA) [80,81,90].…”

Section: Introductionmentioning

confidence: 99%

Geometry smoothing and local enrichment of the finite cell method with application to cemented granular materials

Gorji,

Komodromos,

Garhuom

et al. 2024

Comput Mech

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In recent times, immersed methods such as the finite cell method have been increasingly employed in structural mechanics to address complex-shaped problems. However, when dealing with heterogeneous microstructures, the FCM faces several challenges. Weak discontinuities occur at the interfaces between the different materials, resulting in kinks in the displacements and jumps in the strain and stress fields. Furthermore, the morphology of such composites is often described by 3D images, such as ones derived from X-ray computed tomography. These images lead to a non-smooth geometry description and thus, singularities in the stresses arise. In order to overcome these problems, several strategies are presented in this work. To capture the weak discontinuities at the material interfaces, the FCM is combined with local enrichment. Moreover, the L$$^2$$ 2 -projection is extended and applied to heterogeneous microstructures, transforming the 3D images into smooth level-set functions. All of the proposed approaches are applied to numerical examples. Finally, an application of cemented granular material is investigated using three versions of the FCM and is verified against the finite element method. The results show that the proposed methods are suitable for simulating heterogeneous materials starting from CT scans.

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Section: Introductionmentioning

confidence: 99%

Geometry smoothing and local enrichment of the finite cell method with application to cemented granular materials

Gorji,

Komodromos,

Garhuom

et al. 2024

Comput Mech

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“…However, the numerical modelling of ultrasonic guided wave propagation in solid media exhibiting discontinuities, such as damage, is complex; it requires fine discretisation and is computationally intensive. Even though methods such as the p-version of the finite element method (p-FEM) [12], the isogeometric analysis (IGA) [13] approach, the spectral cell method (SCM) [14], and the time domain spectral element method (SEM) [15] are more efficient and accurate than the classical FEM with linear elements, they are not efficient enough to be used in inverse methods (about half the number of nodes is required to obtain the same accuracy according to [16]). In the end, calling the objective function for each damage case scenario in which the forward solver is used is unfeasible, because computations for even a simple plate can take up to 1 h.…”

Section: Introductionmentioning

confidence: 99%

Simulation of Full Wavefield Data with Deep Learning Approach for Delamination Identification

Ullah,

Kudela,

Ijjeh

et al. 2024

Applied Sciences

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In this work, a novel approach of guided wave-based damage identification in composite laminates is proposed. The novelty of this research lies in the implementation of ConvLSTM-based autoencoders for the generation of full wavefield data of propagating guided waves in composite structures. The developed surrogate deep learning model takes as input full wavefield frames of propagating waves in a healthy plate, along with a binary image representing delamination, and predicts the frames of propagating waves in a plate, which contains single delamination. The evaluation of the surrogate model is ultrafast (less than 1 s). Therefore, unlike traditional forward solvers, the surrogate model can be employed efficiently in the inverse framework of damage identification. In this work, particle swarm optimisation is applied as a suitable tool to this end. The proposed method was tested on a synthetic dataset, thus showing that it is capable of estimating the delamination location and size with good accuracy. The test involved full wavefield data in the objective function of the inverse method, but it should be underlined as well that partial data with measurements can be implemented. This is extremely important for practical applications in structural health monitoring where only signals at a finite number of locations are available.

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“…However, when decoupled geometrical descriptions as in the SCM or the XFEM are employed, special integration rules are applied for elements intersected by a boundary, thus eliminating the diagonal property of the mass matrix. To recover this quality, Joulaian et al [52] proposed to perform HRZ (Hinton, Rock, and Zienkiewicz) lumping [53], a solution later applied by Giraldo and Restrepo in earthquake modeling [54] and also adopted by Mossaiby et al [55] in a GPU implementation of the SCM. As hypothesized in [52] and confirmed in [56], the lumping procedure might introduce some error which negatively affects the convergence of SE, although it guarantees positiveness of the resulting mass coefficients.…”

Section: Introductionmentioning

confidence: 99%

Moment fitted cut spectral elements for explicit analysis of guided wave propagation

Nicoli,

Agathos,

Chatzi

2021

Preprint

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In this work, a method for the simulation of guided wave propagation in solids defined by implicit surfaces is presented. The method employs structured grids of spectral elements in combination to a fictitious domain approach to represent complex geometrical features through singed distance functions. A novel approach, based on moment fitting, is introduced to restore the diagonal mass matrix property in elements intersected by interfaces, thus enabling the use of explicit time integrators. Since this approach can lead to significantly decreased critical time steps for intersected elements, a "leap-frog" algorithm is employed to locally comply with this condition, thus introducing only a small computational overhead. The resulting method is tested through a series of numerical examples of increasing complexity, where it is shown that it offers increased accuracy compared to other similar approaches. Due to these improvements, components of interest for SHM-related tasks can be effectively discretized, while maintaining a performance comparable or only slightly worse than the standard spectral element method.

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The spectral cell method for wave propagation in heterogeneous materials simulated on multiple GPUs and CPUs

Cited by 16 publications

References 40 publications

Geometry smoothing and local enrichment of the finite cell method with application to cemented granular materials

Geometry smoothing and local enrichment of the finite cell method with application to cemented granular materials

Simulation of Full Wavefield Data with Deep Learning Approach for Delamination Identification

Moment fitted cut spectral elements for explicit analysis of guided wave propagation

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