Computer Science / Numerical Analysis

All posts under category "Computer Science / Numerical Analysis"

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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
Banded Householder representation of linear subspaces

Banded Householder representation of linear subspaces

์ด ๋…ผ๋ฌธ์€ ๋Œ€์šฉ๋Ÿ‰ ํ–‰๋ ฌ์˜ ์••์ถ•๊ณผ ํ‘œํ˜„์— ๋Œ€ํ•œ ์ƒˆ๋กœ์šด ์ ‘๊ทผ๋ฒ•์„ ์ œ์‹œํ•˜๋ฉฐ, ํŠนํžˆ ํ•˜์šฐ์Šคํ™€๋” ๋ถ„ํ•ด๋ฅผ ์ด์šฉํ•œ ๋ฐฉ๋ฒ•๋ก ์„ ๊ฐ•์กฐํ•œ๋‹ค. ์ฃผ์š” ๋‚ด์šฉ์€ ๋‹ค์Œ๊ณผ ๊ฐ™๋‹ค: 1. ํ•˜์šฐ์Šคํ™€๋” QR ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ๊ฐœ์š” : ๋…ผ๋ฌธ์€ ๋จผ์ € ํ•˜์šฐ์Šคํ™€๋” QR ์•Œ๊ณ ๋ฆฌ์ฆ˜์ด m ร— n ์ง๊ต ํ–‰๋ ฌ U ๋ฅผ n ๊ฐœ์˜ ํ•˜์šฐ์Šคํ™€๋” ๋ฐ˜์‚ฌ(reflection)์˜ ๊ณฑ์œผ๋กœ ํ‘œํ˜„ํ•˜๋Š” ๋ฐฉ๋ฒ•์„ ์„ค๋ช…ํ•œ๋‹ค. ์ด๋Š” ์ด n(m (n + 1)/2) ๊ฐœ์˜ ๋ถ€๋™ ์†Œ์ˆ˜์  ์—ฐ์‚ฐ์ด ํ•„์š”ํ•˜๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์‹ค์ œ ์‘์šฉ์—์„œ๋Š” ํ–‰๋ ฌ์˜ ๋ฒ”์œ„๋งŒ ์ค‘์š”ํ•˜๋ฉฐ, ๋™์ผํ•œ ๋ฒ”์œ„๋ฅผ ๊ฐ€์ง€๋Š” ๋‹ค๋ฅธ ์ง๊ต ํ–‰๋ ฌ์€ ๋™๋“ฑํ•˜๋‹ค. 2. ๋ฐด๋“œ ํ•˜์šฐ์Šคํ™€๋” ๋ถ„ํ•ด

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
Development and Modelling of High-Efficiency Computing Structure for Digital Signal Processing

Development and Modelling of High-Efficiency Computing Structure for Digital Signal Processing

๋ณธ ๋…ผ๋ฌธ์˜ ํ•ต์‹ฌ ๋‚ด์šฉ์€ ์Šคํ”Œ๋ผ์ธ(spline) ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ํ™œ์šฉํ•œ ๊ณ ์† ์‹ ํ˜ธ ๋ณต์› ์ปดํ“จํŒ… ๊ตฌ์กฐ ๊ฐœ๋ฐœ์— ๋Œ€ํ•œ ๊ฒƒ์ž…๋‹ˆ๋‹ค. ์ด ์—ฐ๊ตฌ๋Š” ๋””์ง€ํ„ธ ์‹ ํ˜ธ ์ฒ˜๋ฆฌ ๋ถ„์•ผ์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•˜๋Š” ์Šคํ”Œ๋ผ์ธ ๋ชจ๋ธ์˜ ๋ฐœ์ „๊ณผ ์ ์šฉ์— ์ค‘์ ์„ ๋‘๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. 1. ์Šคํ”Œ๋ผ์ธ ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ์ค‘์š”์„ฑ ์Šคํ”Œ๋ผ์ธ์€ ๋‹ค์–‘ํ•œ ์ฝ๊ธฐ ์ฒ˜๋ฆฌ ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ๋ณดํŽธ์„ฑ์„ ์ œ๊ณตํ•˜๋ฉฐ, ์šฐ์ˆ˜ํ•œ ๋ฏธ๋ถ„ ๋ฐ ๊ทนํ•œ ํŠน์„ฑ, ๋†’์€ ์ถ”์ • ์ˆ˜๋ ด๋„๋ฅผ ๊ฐ€์ง€๊ณ  ์žˆ์–ด ์‹ ํ˜ธ ๋ถ„์„๊ณผ ๋ณต์›์— ๋„๋ฆฌ ์‚ฌ์šฉ๋˜๊ณ  ์žˆ์Šต๋‹ˆ๋‹ค. ํŠนํžˆ ์Šคํ”Œ๋ผ์ธ์€ ๋‹จ์ˆœํ•œ ํ˜•ํƒœ์™€ ํŒŒ๋ผ๋ฏธํ„ฐ ๊ณ„์‚ฐ, ๊ทธ๋ฆฌ๊ณ  ๋ผ์šด๋“œ ์˜ค๋ฅ˜์— ๋Œ€ํ•œ ์•ฝํ•œ ์˜ํ–ฅ์œผ๋กœ ์ธํ•ด 1์ฐจ์› ๋ฐ ๋‹ค๋ณ€์ˆ˜ ์‹ 

Numerical Analysis Model Computer Science

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