For the determination of lateral velocity or absorption inhomogeneities, methods such as the generalized matrix inversion and its damped versions, for example the stochastic inverse, are usually applied in seismology to travel-time or amplitude anomalies. These methods are not appropriate for the solution of very extensive systems of equations. Reconstruction techniques as developed for computer tomography are suitable for operations with extremely large numbers of equations and unknown parameters. In this paper solutions obtained with the BPT (Back Projection Technique), ART (Algebraic Reconstruction Technique) and SIRT (Simultaneous Iterative Reconstruction Technique) are compared with those obtained from a damped version of the generalized inverse method. Data of 2-D model-seismic experiments are presented for demonstration.
We introduce a new framework of numerical multiscale methods for advection-dominated problems motivated by climate sciences. Current numerical multiscale methods (MsFEM) work well on stationary elliptic problems but have difficulties when the model involves dominant lower order terms. Our idea to overcome the associated difficulties is a semi-Lagrangian based reconstruction of subgrid variability into a multiscale basis by solving many local inverse problems. Globally the method looks like a Eulerian method with multiscale stabilized basis. We show example runs in one and two dimensions and a comparison to standard methods to support our ideas and discuss possible extensions to other types of Galerkin methods, higher dimensions and nonlinear problems.
We implement the ADER-DG numerical method using the CUDA-C language to run the code in a Graphic Processing Unit (GPU). We focus on solving linear hyperbolic partial differential equations where the method can be expressed as a combination of precomputed matrix multiplications becoming a good candidate to be used on the GPU hardware. Moreover, the method is arbitrarily high-order involving intensive work on local data, a property that is also beneficial for the target hardware. We compare our GPU implementation against CPU versions of the same method observing similar convergence properties up to a threshold where the error remains fixed. This behaviour is in agreement with the CPU version but the threshold is larger that in the CPU case. We also observe a big difference when considering single and double precision where in the first case the threshold error is significantly larger. Finally, we did observe a speed up factor in computational time but this is relative to the specific test or benchmark problem
Computing forecasts of hazards, such as tsunamis, requires fast reaction times and high precision, which in turn demands for large computing facilities that are needed only in rare occasions. Cloud computing environments allow to configure largely scalable on-demand computing environments. In this study, we tested two of the major cloud computing environments for parallel scalability for relevant prototypical applications. These applications solve stationary and non-stationary partial differential equations by means of finite differences and finite elements. These test cases demonstrate the capacity of cloud computing environments to provide scalable computing power for typical tasks in geophysical applications. As a proof-of-concept example of an instant computing application for geohazards, we propose a workflow and prototypical implementation for tsunami forecasting in the cloud. We demonstrate that minimal on-site computing resources are necessary for such a forecasting environment. We conclude by outlining the additional steps necessary to implement an operational tsunami forecasting cloud service, considering availability and cost.
The simulation of fluid dynamic problems often involves solving large-scale saddle-point systems.Their numerical solution with iterative solvers requires efficient preconditioners. Low-rank updates canadapt standard preconditioners to accelerate their convergence. We consider a multiplicative low-rank cor-rection for pressure Schur complement preconditioners that is based on a (randomized) low-rank approxi-mation of the error between the identity and the preconditioned Schur complement. We further introducea relaxation parameter that scales the initial preconditioner. This parameter can improve the initial pre-conditioner as well as the update scheme. We provide an error analysis for the described update method.Numerical results for the linearized Navier-Stokes equations in a model for atmospheric dynamics on twodifferent geometries illustrate the action of the update scheme. We numerically analyze various parametersof the low-rank update with respect to their influence on convergence and computational time.
MSC codes. 65F08, 65F10, 65N22, 65F55
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