1,720,988 research outputs found
High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes
Full text linkWe propose and analyze a high-order Discontinuous Galerkin Finite Element Method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal and polyhedral elements. We analyze the well posedness of the resulting formulation, prove hp-version error a-priori estimates, and present a dispersion analysis, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion properties. The theoretical estimates are confirmed through various two-dimensional numerical verifications
A discontinuous Galerkin time integration scheme for second order differential equations with applications to seismic wave propagation problems
Full text linkIn this work, we present a high-order Discontinuous Galerkin time integration scheme for second-order (in time) differential systems that typically arise from the space discretization of the elastodynamics equation. By rewriting the original equation as a system of first-order differential equations we introduce the method and show that the resulting discrete formulation is well-posed, stable, and retains a super-optimal rate of convergence with respect to the discretization parameters, namely the time step and the polynomial approximation degree. A set of two-and three-dimensional numerical experiments confirm the theoretical bounds. Finally, the method is applied to real geophysical simulations
3D Ground Response Analysis of Simplified Kutch Basin by Spectral Element Method
No full textThe damage pattern observed during the 1819 Kutch earthquake and 2001 Bhuj earthquake of magnitude Mw>7.7 in India implied the significance of the effect of Kutch basin on seismic ground motion. In the present study, the Kutch rift basin is modeled as a simplified rectangular basin of size 150km × 90km × 1.5km. The shear wave velocity of the Kutch region varies from 300m/s at the surface to 800m/s at the depth of 60m. Three-dimensional ground response analysis is carried out for the simplified Kutch basin subjected to ricker wave, using the spectral element code SPEED. The soil medium is modeled through visco-elastic soil model, where the damping is represented by Quality factor. It is found out from the numerical analysis that maximum amplification of 3.6 times occurs at the corner of the basin where interference of waves reflected from multiple edges happen. The long period structures with fundamental period in the range of 1.5-2.5s located near the basin edge are found to be significantly affected by the basin effect
Unmapped Tent Pitching Schemes by Waveform Relaxation
No full textThe mapped tent pitching algorithm (MTP) is a very advanced domain decomposition strategy for the parallel solution of hyperbolic problems
A high-order discontinuous Galerkin approach to the elasto-acoustic problem
Full text linkWe address the spatial discretization of an evolution problem arising from the coupling of elastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid (elastic) and fluid (acoustic) domains. We state and prove a well-posedness result for the strong formulation of the problem, present a stability analysis for the semi-discrete formulation, and finally prove an a priori hp-version error estimate for the resulting formulation in a suitable (mesh-dependent) energy norm. We also discuss the time integration scheme employed to obtain the fully discrete system. The convergence results are validated by numerical experiments carried out in a two-dimensional setting
Simulation of three-dimensional elastoacoustic wave propagation based on a Discontinuous Galerkin spectral element method
No full textIn this article, we present a numerical discretization of the coupled elastoacoustic wave propagation problem based on a discontinuous Galerkin spectral element approach in a three-dimensional setting. The unknowns of the coupled problem are the displacement field and the velocity potential, in the elastic and the acoustic domains, respectively, thereby resulting in a symmetric formulation. After stating the main theoretical results, we assess the performance of the method by convergence tests carried out on both matching and nonmatching grids, and we simulate realistic scenarios where elastoacoustic coupling occurs. In particular, we consider the case of Scholte waves, the scattering of elastic waves by an underground acoustic cavity, and a problem of marine seismic exploration. Numerical simulations are carried out by means of the code SPEED, available at http://speed.mox.polimi.it
A Virtual Element Method for the Wave Equation on Curved Edges in Two Dimensions
Full text linkIn this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as well as internal interfaces corresponding to the change of some mechanical parameters. As opposite to the classic and isoparametric Finite Element approaches, where the geometry of the domain is approximated respectively by piecewise straight lines and by higher order polynomial maps, in the proposed method the geometry is exactly represented, thus ensuring a highly accurate numerical solution. Indeed, if in the former approach the geometrical error might deteriorate the quality of the numerical solution, in the latter approach the curved interfaces/boundaries are approximated exactly guaranteeing the expected order of convergence for the numerical scheme. Theoretical results and numerical findings confirm the validity of the proposed approach
Elasto-acoustic modeling and simulation for the seismic response of structures: The case of the Tahtalı dam in the 2020 Izmir earthquake
No full textAs a mean to assess the risk dam structures are exposed to during earthquakes, we employ an abstract mathematical, three dimensional, elasto-acoustic coupled wave-propagation model taking into account (i) the dam structure itself, embedded into (ii) its surrounding topography, (iii) different material soil layers, (iv) the seismic source as well as (v) the reservoir lake filled with water treated as an acoustic medium. As a case study for extensive numerical simulations we consider the magnitude 7 seismic event of the 30th of October 2020 taking place in the Icarian Sea (Greece) and the Tahtalı dam around 30 km from there (Turkey). A challenging task is to resolve the multiple length scales that are present due to the huge differences in size between the dam building structure and the area of interest, considered for the propagation of the earthquake. Interfaces between structures and highly non-conforming meshes on different scales are resolved by means of a discontinuous Galerkin approach. The seismic source is modeled using inversion data about the real fault plane. Ultimately, we perform a real data driven, multi-scale, full source-to-site, physics based simulation based on the discontinuous Galerkin spectral element method, which allows to precisely validate the ground motion experienced along the Tahtalı dam, comparing the synthetic seismograms against actually observed ones. A comparison with a more classical computational method, using a plane wave with data from a deconvolved seismogram reading as an input, is discussed
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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