# Alexey Kononov's research while affiliated with Delft University of Technology and other places

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## Publications (8)

The finite-difference method on rectangular meshes is widely used for time-domain modelling of the wave equation. It is relatively easy to implement high-order spatial discretization schemes and parallelization. Also, the method is computationally efficient. However, the use of finite elements on tetrahedral unstructured meshes is more accurate in...

Modeling and imaging techniques for geophysics are extremely demanding in terms of computational resources. Seismic data attempt to resolve smaller scales and deeper targets in increasingly more complex geologic settings. Finite elements enable accurate simulation of time-dependent wave propagation in heterogeneous media. They are more costly than...

Finite-element modelling of seismic wave propagation on tetrahedra requires meshes that accurately follow interfaces between impedance contrasts or surface topography and have element sizes proportional to the local velocity. We explain a mesh generation approach by example. Starting from a finite-difference representation of the velocity model, tr...

SUMMARY Present-day computers allow for realistic 3D simulations of seismic wave propagation, as well as migration and inversion of seismic data with numerical solutions of the full wave equation. The finitedifference method is popular because of its simplicity but suffers from accuracy degradation for complex models with sharp interfaces between l...

We investigate the parallel performance of an iterative solver for 3D heterogeneous Helmholtz problems related to applications in seismic wave propagation. For large 3D problems, the computation is no longer feasible on a single processor, and the memory requirements increase rapidly. Therefore, parallelization of the solver is needed. We employ a...

## Citations

... The pressure then is recorded at a 300m−offset receiver situated 250m above the interface, and the signal is compared to an exact solution. More details about this benchmark are given by Minisini et al. (2012) and Zhebel et al. (2014). Figure 2 shows curves of relative errors as function of the characteristic mesh size and the running time. ...

... The finite-difference method is widely used in the oil industry because it is relatively easy to code up and optimize. The finite-element method is computationally more demanding but may offer better accuracy at a given cost in the presence of topography and large impedance contrast, but only if the mesh follows the interfaces between different rock types (Kononov et al. 2012;Zhebel et al. 2014). ...

... If the topography is gradual and smooth, locally orthogonal boundary-fitted coordinates will work (e.g., Tessmer and Kosloff, 1994;Ruud, 1998, 2002;De la Puente et al., 2014). The more general case requires a finite-element approach (e.g., Komatitsch and Vilotte, 1998;Etienne et al., 2010;Zhebel et al., 2011) or a mimetic finite-difference method (for a review, see Lipnikov et al., 2014). Both tend to increase the computing cost. ...

... For finite-differences and finite-elements algorithms running on Intel Xeon and Intel Xeon Phi processors, Zhebel et al. [12] compared scalability of unmodified codes. Scalability analyses are out of the scope of this work, yet not excluded from future lines to evaluate. ...

... Such sets of points are known up to k = 9 for triangles and k = 4 for tetrahedra, and due to their diagonal mass matrix, they can be used for fast fully explicit numerical wave simulations (Chin-Joe-Kong et al., 1999;Mulder et al., 2013;Geevers et al., 2018b, a;Cui et al., 2017;Liu et al., 2017). These elements have been compared with finite-difference schemes and have favorable results for the forward wave propagation when interior complexity and topography are present that can be adequately modeled with unstructured tetrahedra (Zhebel et al., 2014). However, to the authors' knowledge these elements have not been used in peer-reviewed literature to perform seismic inversions. ...

... Inside the``fine"" part, however, the method loops over p local LF steps of size \Delta t/p, where p \geq H/h \mathrm{ is a positive integer. When combined with a mass-lumped conforming [11,10] or DG FE discretization [23] in space, the resulting method is truly explicit and inherently parallel; it was successfully applied to three-dimensional seismic wave propagation [31]. A multilevel version was later proposed [13] and achieved high parallel efficiency on an HPC architecture [41]. ...

... The geometric multigrid needs nested grids to construct operational operators. In this paper, we adopt a two-dimensional (2D) semi-coarsening strategy [52,53] to obtain a series of nested grids. Refer to Figure 2, the mesh coarsening is performed only in x-and y-direction, while the mesh in z-direction is kept unchanged. ...