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A well-balanced finite volume scheme for 1D hemodynamic simulations

A well-balanced finite volume scheme for 1D hemodynamic simulations

๋ณธ ๋…ผ๋ฌธ์€ ํ˜ˆ๋ฅ˜ ํ๋ฆ„์˜ 1์ฐจ์› ๋ชจ๋ธ ๋ฐ ์ˆ˜์น˜ ์‹œ๋ฎฌ๋ ˆ์ด์…˜์— ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ๋‹ค. ํŠนํžˆ, ๋น„์ผ์ • ํƒ„์„ฑ์„ฑ์„ ๊ฐ€์ง„ ๋™๋งฅ์—์„œ์˜ ํ˜ˆ๋ฅ˜๋ฅผ ์ •ํ™•ํ•˜๊ฒŒ ๋ชจ๋ธ๋งํ•˜๊ณ  ์‹œ๋ฎฌ๋ ˆ์ด์…˜ํ•˜๊ธฐ ์œ„ํ•œ ๊ท ํ˜• ์žกํžŒ ์œ ํ•œ ์ฒด์  ์Šคํ‚ด์„ ์ œ์•ˆํ•œ๋‹ค. 1. ๋ณด์กดํ˜• ์งˆ๋Ÿ‰ ๋ฐ ์šด๋™๋Ÿ‰ ๋ฐฉ์ •์‹ ๋…ผ๋ฌธ์€ ๋น„์ผ์ • ํƒ„์„ฑ์„ฑ์„ ๊ฐ€์ง„ ๋™๋งฅ์—์„œ์˜ ํ˜ˆ๋ฅ˜ ํ๋ฆ„์„ ๋ชจ๋ธ๋งํ•˜๊ธฐ ์œ„ํ•ด ๋ณด์กดํ˜• ์งˆ๋Ÿ‰ ๋ฐ ์šด๋™๋Ÿ‰ ๋ฐฉ์ •์‹์„ ๊ณ ๋ คํ•˜๊ณ  ์žˆ๋‹ค. ์ด ๋ฐฉ์ •์‹๋“ค์€ ์ผ๋ฐ˜์ ์œผ๋กœ ์‚ฌ์šฉ๋˜๋Š” ํ˜•ํƒœ์™€ ๋‹ฌ๋ฆฌ ๋ณด์ˆ˜์ ์ธ ํ˜•ํƒœ๋กœ ์žฌํ‘œํ˜„๋˜์–ด ์žˆ์œผ๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ์ •์  ์ƒํƒœ๋ฅผ ๋ณด์กดํ•˜๋Š” ๊ท ํ˜• ์žกํžŒ ์Šคํ‚ด์„ ๋„์ž…ํ•  ์ˆ˜ ์žˆ๊ฒŒ ๋œ๋‹ค. 2. ๊ท ํ˜• ์žกํžŒ ์œ ํ•œ ์ฒด์ 

Mathematics Numerical Analysis Computer Science
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An introduction to ML(n)BiCGStab

1. ์„œ๋ก  ๋ฐ ๋ฐฐ๊ฒฝ ML(n)BiCGStab๋Š” BiCGStab ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ์ž์—ฐ์Šค๋Ÿฌ์šด ์ผ๋ฐ˜ํ™”๋กœ, Yeung๊ณผ Chan์— ์˜ํ•ด 1999๋…„ ์†Œ๊ฐœ๋˜์—ˆ๋‹ค. ์ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ์—ฌ๋Ÿฌ ์‹œ์ž‘ ๋žœํฌ๋กœ์Šค ๊ณผ์ •์„ ๊ธฐ๋ฐ˜์œผ๋กœ ํ•˜๋ฉฐ, van der Vorst์˜ BiCGStab์—์„œ ํŒŒ์ƒ๋˜์—ˆ์ง€๋งŒ ๋” ์•ˆ์ •์ ์ด๊ณ  ํšจ์œจ์ ์ธ ์„ฑ๋Šฅ์„ ์ œ๊ณตํ•œ๋‹ค. Sonneveld์™€ van der Vorst๊ฐ€ CGS์™€ BiCGStab๋ฅผ ๊ตฌ์„ฑํ•˜๋Š” ๋ฐ ์‚ฌ์šฉํ•œ ๊ธฐ๋ฒ•์ด ML(n)BiCGStab์—๋„ ์ ์šฉ๋˜์—ˆ๋‹ค. 2. ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ์œ ๋„ ๋ฐ ๊ตฌ์กฐ ML(n)BiCGStab๋Š” ์—ฌ๋Ÿฌ ์‹œ์ž‘ ๋ฒกํ„ฐ๋ฅผ ์ด์šฉํ•˜์—ฌ Kryl

Computer Science Mathematics Numerical Analysis
Series Prediction based on Algebraic Approximants

Series Prediction based on Algebraic Approximants

์ด ๋…ผ๋ฌธ์€ ๋ณต์žกํ•œ ํ•จ์ˆ˜์˜ ์‹œํ€€์Šค ์˜ˆ์ธก์„ ์œ„ํ•œ ์ƒˆ๋กœ์šด ์ ‘๊ทผ๋ฒ•์„ ์ œ์‹œํ•˜๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. ํŠนํžˆ, ์ด ์—ฐ๊ตฌ๋Š” ๋Œ€์ˆ˜์  ๊ทผ์‚ฌ์™€ ํ—ˆ๋ฏธํŠธ ํŒŒ๋ฐ ๋‹คํ•ญ์‹(HPP)์— ์ค‘์ ์„ ๋‘๊ณ  ์žˆ์œผ๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ๋ณต์žกํ•œ ์‹œํ€€์Šค๋ฅผ ํšจ๊ณผ์ ์œผ๋กœ ์˜ˆ์ธกํ•  ์ˆ˜ ์žˆ๋Š” ๋ฐฉ๋ฒ•๋ก ์„ ๊ฐœ๋ฐœํ•˜์˜€์Šต๋‹ˆ๋‹ค. 1. ๋Œ€์ˆ˜์  ๊ทผ์‚ฌ์˜ ๊ฐœ๋… ๋…ผ๋ฌธ์€ ๋Œ€์ˆ˜์  ๊ทผ์‚ฌ๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๋ณต์žกํ•œ ํ•จ์ˆ˜์˜ ์ง€์ˆ˜ ๊ธ‰์ˆ˜๋ฅผ ๊ทผ์‚ฌํ•˜๋Š” ๋ฐฉ๋ฒ•์— ๋Œ€ํ•ด ์„ค๋ช…ํ•ฉ๋‹ˆ๋‹ค. ์ด๋Š” ํ—ˆ๋ฏธํŠธ ํŒŒ๋ฐ ๋‹คํ•ญ์‹(HPP)์„ ์ด์šฉํ•ด ์ˆ˜ํ–‰๋˜๋ฉฐ, HPP๋Š” ์ฃผ์–ด์ง„ ํ•จ์ˆ˜ f ๊ฐ€ ์ง€์ˆ˜ ๊ธ‰์ˆ˜ ํ˜•ํƒœ๋กœ ํ‘œํ˜„๋  ๋•Œ, ์ด๋ฅผ ๊ทผ์‚ฌํ•˜๋Š” ๋‹คํ•ญ์‹ ์ง‘ํ•ฉ์ž…๋‹ˆ๋‹ค. 2. ํ—ˆ๋ฏธํŠธ ํŒŒ๋ฐ ๋‹คํ•ญ์‹์˜ ๊ตฌ์„ฑ

Mathematics Physics

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