By Barry Koren, Kees Vuik
The objective of the current e-book is to teach, in a huge and but deep manner, the cutting-edge in computational technological know-how and engineering. Examples of issues addressed are: quick and exact numerical algorithms, model-order relief, grid computing, immersed-boundary tools, and particular computational tools for simulating a large choice of difficult difficulties, difficulties akin to: fluid-structure interplay, turbulent flames, bone-fracture therapeutic, micro-electro-mechanical structures, failure of composite fabrics, typhoon surges, particulate flows, etc. the most profit provided to readers of the booklet is a well-balanced, up to date evaluate over the sphere of computational technology and engineering, via in-depth articles by way of experts from the separate disciplines.
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Extra info for Advanced Computational Methods in Science and Engineering (Lecture Notes in Computational Science and Engineering)
5, with the second- and fourth-order discretizations. We observe the asymptotic h-independent convergence rate for the iterative solver on the finer grids; with fixed wavenumber and h decreasing, approximately the same number of iterations is needed to satisfy the termination criterion, for both discretizations. However, on the coarse grids, where we have kh > 1, we see a drastic increase in the number of iterations needed to converge, especially for the second-order discretization. Shifted-Laplacian Preconditioners for Heterogeneous Helmholtz Problems (a) k = 40 41 (b) k = 80 Fig.
Plessix Absorption layer e Ω e Γ 1000m/s 2000 m/s Ω 1000 m/s Γ Physical domain Fig. 1 A 2D domain with ABL in the case of a regular heterogeneous wedge medium. 2 Discretization The equations are discretized here either by a second- or a fourth-order finitedifference scheme, resulting in the linear system: Ah φh = bh , (4) where φh and bh represent the discrete frequency-domain pressure field and the source, respectively. In a heterogeneous medium, the smallest velocity is usually selected based on the representative wavelength, λ f .
An efficient numerical solution technique should be robust with respect to this kind of feature. The absorption layers (denoted by Ω e ) are attached to the physical domain, Ω , (see Figure 1). 25 x − xd xe − xd 2 2 , x ∈ Ω e, (2) where point xd is a point at the boundary, Γ , and xe a point at Γ e (see Figure 1). The boundary conditions at the boundary Γ e are in the form of first- or second-order absorbing boundary conditions. We use approximate radiation (or non-reflecting) boundary conditions at the artificial boundary.