{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:33:26Z","timestamp":1760236406570,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,26]],"date-time":"2021-11-26T00:00:00Z","timestamp":1637884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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 \u201ccross\u201d 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 \u00d7 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.<\/jats:p>","DOI":"10.3390\/a14120343","type":"journal-article","created":{"date-parts":[[2021,11,28]],"date-time":"2021-11-28T22:19:16Z","timestamp":1638137956000},"page":"343","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Algorithmic Design of an FPGA-Based Calculator for Fast Evaluation of Tsunami Wave Danger"],"prefix":"10.3390","volume":"14","author":[{"given":"Mikhail","family":"Lavrentiev","sequence":"first","affiliation":[{"name":"Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia"}]},{"given":"Konstantin","family":"Lysakov","sequence":"additional","affiliation":[{"name":"Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia"}]},{"given":"Andrey","family":"Marchuk","sequence":"additional","affiliation":[{"name":"Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia"},{"name":"Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090 Novosibirsk, Russia"}]},{"given":"Konstantin","family":"Oblaukhov","sequence":"additional","affiliation":[{"name":"Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia"}]},{"given":"Mikhail","family":"Shadrin","sequence":"additional","affiliation":[{"name":"Institute of Automation and Electrometry SB RAS, 630090 Novosibirsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,26]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Lavrentiev, M., Lysakov, K., Marchuk, A., Oblaukhov, K., and Shadrin, M. (2020). Hardware Acceleration of Tsunami Wave Propagation Modeling in the Southern Part of Japan. Appl. Sci., 10.","key":"ref_1","DOI":"10.3390\/app10124159"},{"unstructured":"(2021, November 20). IEEE 1364-2001\u2014IEEE Standard Verilog Hardware Description Language. Available online: https:\/\/standards.ieee.org\/standard\/1364-2001.html.","key":"ref_2"},{"doi-asserted-by":"crossref","unstructured":"MacCormack, R.W., and Paullay, A.J. (1972, January 17\u201319). Computational Efficiency Achieved by Time Splitting of Finite\u2013Difference Operators. Proceedings of the 10th Aerospace Sciences Meeting, San Diego, CA, USA. AIAA Paper.","key":"ref_3","DOI":"10.2514\/6.1972-154"},{"unstructured":"Krause, E., Shokin, Y., and Shokina, N. (2008). Mathematical Modeling in Application to Regional Tsunami Warning Systems Operations. Computational Science and High Performance Computing III: The 3rd Russian-German Advanced Research Workshop, Springer Science & Business Media.","key":"ref_4"},{"unstructured":"(2021, November 20). Vitis High-Level Synthesis User Guide. Available online: https:\/\/www.xilinx.com\/support\/documentation\/sw_manuals\/xilinx2021_1\/ug1399-vitis-hls.pdf.","key":"ref_5"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1134\/S1995423915040047","article-title":"Estimating Tsunami Wave Height over a Sloping Bottom in the Ray Approximation","volume":"8","author":"Marchuk","year":"2015","journal-title":"Numer. Anal. Appl."},{"key":"ref_7","first-page":"70","article-title":"Benchmark solutions for tsunami wave fronts and rays. Part 2: Parabolic bottom topography","volume":"36","author":"Marchuk","year":"2017","journal-title":"Sci. Tsunami Hazards"},{"unstructured":"Titov, V.V., and Gonzalez, F.I. (1997). Implementation and Testing of the Method of Splitting Tsunami (MOST) Model, Pacific Marine Environmental Laboratory. NOAA Technical Memorandum ERL PMEL-112.","key":"ref_8"},{"unstructured":"Stoker, J.J. (1957). Water Waves. The Mathematical Theory with Applications, Interscience publishers.","key":"ref_9"},{"unstructured":"(2021, November 20). JODC 500 m Gridded Bathymetry Data. Available online: https:\/\/jdoss1.jodc.go.jp\/vpage\/depth500_file.html.","key":"ref_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1007\/s00024-012-0519-z","article-title":"Modeling of the 2011 Japan Tsunami: Lessons for Near-Field Forecast","volume":"170","author":"Wei","year":"2013","journal-title":"Pure Appl. Geophys."},{"unstructured":"Grilli, S.T., Harris, J.C., Bakhsh, T.T., Kirby, J.T., Shi, F., Masterlark, T.L., and Kyriakopoulos, C. (2012, January 17\u201322). Numerical simulation of the 2011 Tohoku tsunami: Comparison with field observations and sensitivity to model parameters. Proceedings of the Twenty-second (2012) International Offshore and Polar Engineering Conference, Rhodes, Greece.","key":"ref_12"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/12\/343\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:36:24Z","timestamp":1760168184000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/12\/343"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,26]]},"references-count":12,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["a14120343"],"URL":"https:\/\/doi.org\/10.3390\/a14120343","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2021,11,26]]}}}