Algorithmic Design of an FPGA-Based Calculator for Fast Evaluation of Tsunami Wave Danger

Events of a seismic nature followed by catastrophic floods caused by tsunami waves (the incidence of which has increased in recent decades) have an important impact on the populations of littoral regions. On the coast of Japan and Kamchatka, it takes nearly 20 min for tsunami waves to approach the n...

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Published in:	Algorithms Vol. 14; no. 12; p. 343
Main Authors:	Lavrentiev, Mikhail, Lysakov, Konstantin, Marchuk, Andrey, Oblaukhov, Konstantin, Shadrin, Mikhail
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.12.2021
Subjects:	algorithm implementation Algorithms Catastrophic events Chips (memory devices) Computational grids Data processing Earthquakes Exact solutions Field programmable gate arrays High level synthesis Littoral environments MacCormack scheme numerical modeling Ocean floor Power supply Propagation Seismic activity Shallow water Simulation Software tsunami wave Tsunamis Wave fronts Wave propagation United States > US Japan
ISSN:	1999-4893, 1999-4893
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Abstract	Events of a seismic nature followed by catastrophic floods caused by tsunami waves (the incidence of which has increased in recent decades) have an important impact on the populations of littoral regions. On the coast of Japan and Kamchatka, it takes nearly 20 min for tsunami waves to approach the nearest dry land after an offshore seismic event. This paper addresses an important question of fast simulation of tsunami wave propagation by mapping the algorithms in use in field-programmable gate arrays (FPGAs) with the help of high-level synthesis (HLS). Wave propagation is described by the shallow water system, and for numerical treatment the MacCormack scheme is used. The MacCormack algorithm is a direct difference scheme at a three-point stencil of a “cross” type; it happens to be appropriate for FPGA-based parallel implementation. A specialized calculator was designed. The developed software was tested for precision and performance. Numerical tests computing wave fronts show very good agreement with the available exact solutions (for two particular cases of the sea bed topography) and with the reference code. As the result, it takes just 17.06 s to simulate 1600 s (3200 time steps) of the wave propagation using a 3000 × 3200 computation grid with a VC709 board. The step length of the computational grid was chosen to display the simulation results in sufficient detail along the coastline. At the same time, the size of data arrays should provide their free placement in the memory of FPGA chips. The rather high performance achieved shows that tsunami danger could be correctly evaluated in a few minutes after seismic events.
AbstractList	Events of a seismic nature followed by catastrophic floods caused by tsunami waves (the incidence of which has increased in recent decades) have an important impact on the populations of littoral regions. On the coast of Japan and Kamchatka, it takes nearly 20 min for tsunami waves to approach the nearest dry land after an offshore seismic event. This paper addresses an important question of fast simulation of tsunami wave propagation by mapping the algorithms in use in field-programmable gate arrays (FPGAs) with the help of high-level synthesis (HLS). Wave propagation is described by the shallow water system, and for numerical treatment the MacCormack scheme is used. The MacCormack algorithm is a direct difference scheme at a three-point stencil of a “cross” type; it happens to be appropriate for FPGA-based parallel implementation. A specialized calculator was designed. The developed software was tested for precision and performance. Numerical tests computing wave fronts show very good agreement with the available exact solutions (for two particular cases of the sea bed topography) and with the reference code. As the result, it takes just 17.06 s to simulate 1600 s (3200 time steps) of the wave propagation using a 3000 × 3200 computation grid with a VC709 board. The step length of the computational grid was chosen to display the simulation results in sufficient detail along the coastline. At the same time, the size of data arrays should provide their free placement in the memory of FPGA chips. The rather high performance achieved shows that tsunami danger could be correctly evaluated in a few minutes after seismic events.
Author	Oblaukhov, Konstantin Lavrentiev, Mikhail Lysakov, Konstantin Marchuk, Andrey Shadrin, Mikhail
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Copyright	2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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References	ref_1 ref_3 ref_2 Marchuk (ref_6) 2015; 8 ref_9 Marchuk (ref_7) 2017; 36 ref_8 ref_12 ref_5 ref_10 ref_4 Wei (ref_11) 2013; 170
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SubjectTerms	algorithm implementation Algorithms Catastrophic events Chips (memory devices) Computational grids Data processing Earthquakes Exact solutions Field programmable gate arrays High level synthesis Littoral environments MacCormack scheme numerical modeling Ocean floor Power supply Propagation Seismic activity Shallow water Simulation Software tsunami wave Tsunamis Wave fronts Wave propagation
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