Mikhail M. Lavrentiev

Modern Hardware to Simulate Tsunami Wave Propagation

Problem of tsunami risks evaluation, assessment and mitigation is here addressed. Modern computational technologies are able to calculate accurately tsunami wave propagation over the deep ocean provided that initial displacement (perturbation of the sea bed at tsunami source) is known. Modern deep ocean tsunameters provide direct measurement of the passing tsunami wave in the real time mode, which help to estimate initial displacement parameters right after the tsunami wave is recorded at one of the deep ocean buoys. Therefore, fast tsunami propagation code that can calculate tsunami evolution from estimated model source becomes critical for timely evacuation decision for many coastal communities in case of a strong tsunami. In this paper we discuss a part of MOST (Method of Splitting Tsunami) software package, which has been accepted by the USA National Ocean and Atmosphere Administration as the basic tool to calculate tsunami wave propagation and to evaluate of inundation parameters. Our main objectives are to speed up the existing sequential program, and to adapt this program for shared memory systems (OpenMP), CELL BE architecture and GPU. For caring out this research we use SMP server and a system build on IBM CELL BE CPU. We also use NVIDIA Tesla C1060 board which acts as co-processor for CPU. Optimization of the existing parallel and sequential code for the task of tsunami wave propagation modeling as well as an adaptation of this code for GPU and CELL BE processor is discussed. The obtained results are up to 170 times performance gain for one time step. These are very promising.

Implementation of Mac-Cormack scheme for the fast calculation of tsunami wave propagation

In this paper, we continue the discussion about of fast numerical simulation of tsunami wave propagation. In case of seismic event offshore Japan, tsunami approaches the nearest shore in approximately 20 minutes. As the calculation of tsunami wave propagation normally serves as a part of any warning system, speeding up this software results in overall better performance for tsunami warning. Implementation of the Mac-Cormack scheme to solve the shallow water system is here described. Field programmable gates array (FPGA) microchip is used to achieve better performance. The numerical solution is compared with the available exact solution to the problem considered.

Optimal structure of the cost functional for coastal profile evolution problems

Behaviour-oriented diffusion models, available in literature, reasonably describe the time evolution of the cross-shore position of coastal profiles (depth as a function of the distance to shore line). In previous works, we were able to identify the time-independent, but space-dependent coefficients, in 1D (and later in 2D) behaviour-oriented diffusion models for the time dynamics of long-term coastal profile evolution. Models with such coefficients even predict the depth profile evolution for some years ahead. We now focus on the structure of the so-called Cost Functional (CF), which is used to identify the coefficients above. An optimized version of CF provides smaller relative error predicting the depth profile evolution.

Determination of initial tsunami wave shape at sea surface

Any Tsunami Early Warning System (TEWS) should provide reliable prediction of the wave parameters as early as possible. Numerical calculation of the tsunami wave propagation over the particular part of the ocean can be implemented rather efficiently using modern high-performance system. It is possible when the initial wave shape at tsunami source is given. In this paper we discuss and show the fast algorithm for reconstructing the initial sea surface displacement at tsunami source. Based on the Fourier approximation theory, the presented algorithm treats the measured wave profile as a linear combination of synthetic (calculated) waves from the so-called unit sources. Using an artificial bathymetry, we evaluate the algorithm parameters focusing on its precision and performance. Moreover, a large tsunami sources (several hundred kilometers long) are also simulated.

Modern simulation tools for real time numerical simulation of ocean-related processes

In this paper we focus on two particular ocean-related problems, valuable progress in which is expected due to extended facilities of the modern computer architectures. The first one concerns real time tsunami risk mitigation by using the advantages of such computer architectures as are Graphic Processing Units (GPU) and Field Programmable Gates Arrays (FPGA). Among many important aspects of tsunami simulation we study the time consumable calculation of the wave propagation over a given water area. A comparison of performances achieved at a range of architectures is given. Secondly, we discuss the coastal profile evolution. As it has been found relatively recently, behavior-oriented diffusion models reasonably describe the time evolution of the cross-shore position of coastal profiles. Two time-independent coefficients in the governing equation, which embody the relevant physical properties, are identified simultaneously. Earlier, the authors have validated and calibrated numerically the proposed model, processing two sets of real data, the first one being measured over 10 years at Duck, in North Carolina (USA), the second one obtained over 39 years measurements at Delfland (Holland). Here, the model dependence on the alongshore position of the observation point is studied. The coefficients of the model equation are determined by means of a certain iteration process. As it was observed, the achieved convergence is now better than when several separate observations along the coast are involved.

An intelligent workstation for a tsunami expert

This work is devoted to development of intelligent workstation for tsunami expert. Our main goal is the architecture design and implementation of a software package which will be used to combine a lot of different tsunami modeling algorithms in one place. Also it should provide a convenient interface for data management. In our research we will describe a modular architecture of workstation and its implementation, which can be used for described purposes. Also we have built in a module for calculating the propagation of tsunami waves based on optimized MOST package [6, 7]

Singular Perturbations of Parabolic Equations With or Without Boundary Layers

Singular perturbations of partial differential equations (PDEs) are encountered due to the nature of certain physical models (e.g., small viscosity in Navier-Stokes equations), or to analyze some asymptotic limiting behavior (long time, long distances). In such cases, sometimes, certain usually nondimensional groups of terms are first identified, e.g., electron to ion mass ratio. Besides, singular perturbations are encountered for regularization purposes, e.g., in the numerical treatment of hyperbolic or ultraparabolic PDEs, like the Fokker-Planck equation, through parabolic regularization.