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An Efficient Multilevel Preconditioned Nonlinear Conjugate Gradient Method for Incremental Potential Contact

์ž‘์„ฑ์ž
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์ €์ž

Yu Zhang, Xing Shen, Kemeng Huang, Wei Chen, Yin Yang, Taku Komura, Tiantian Liu, Xingang Pan

๐Ÿ’ก ๊ฐœ์š”

๋ณธ ๋…ผ๋ฌธ์€ ๊ณ„์‚ฐ ๋น„์šฉ์ด ๋†’์€ Incremental Potential Contact (IPC) ์‹œ๋ฎฌ๋ ˆ์ด์…˜์˜ ํšจ์œจ์„ฑ์„ ๋†’์ด๊ธฐ ์œ„ํ•ด ๋‹ค๋‹จ๊ณ„ ์‚ฌ์ „์กฐ๊ฑด์ด ์ ์šฉ๋œ ๋น„์„ ํ˜• ์ผค๋ ˆ ๊ธฐ์šธ๊ธฐ๋ฒ•(MAS-PNCG)์„ ์ œ์•ˆํ•ฉ๋‹ˆ๋‹ค. ํ•ต์‹ฌ ๊ธฐ์ˆ ์€ ํฌ์†Œ ์ž…๋ ฅ ์šฐ๋“œ๋ฒ„๋ฆฌ ์—…๋ฐ์ดํŠธ๋ฅผ ์‚ฌ์šฉํ•˜์—ฌ ๋น ๋ฅด๊ฒŒ ๋ณ€ํ™”ํ•˜๋Š” ์ ‘์ด‰ ์ง‘ํ•ฉ์— ์ ์‘์ ์œผ๋กœ ์‚ฌ์ „์กฐ๊ฑด๊ธฐ๋ฅผ ์—…๋ฐ์ดํŠธํ•จ์œผ๋กœ์จ, ๋ฐ˜๋ณต์ ์ธ ์žฌ๊ตฌ์ถ• ๋น„์šฉ์„ ์ตœ์†Œํ™”ํ•˜๋Š” ๊ฒƒ์ž…๋‹ˆ๋‹ค. ๋˜ํ•œ, ํ—ค์„ธ์•ˆ ์ •๋ณด๋ฅผ ํ™œ์šฉํ•œ 2D ๋ถ€๋ถ„ ๊ณต๊ฐ„ ์ตœ์†Œํ™”์™€ ๋ณด์กด์  CCD ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ์ˆ˜๋ ด ์†๋„์™€ ์•ˆ์ •์„ฑ์„ ํ–ฅ์ƒ์‹œ์ผฐ์Šต๋‹ˆ๋‹ค.

๐Ÿ”‘ ์‹œ์‚ฌ์  ๋ฐ ํ•œ๊ณ„

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๋‹ค๋‹จ๊ณ„ ์‚ฌ์ „์กฐ๊ฑด ๋ถ€์—ฌ ๊ธฐ๋ฒ•์„ ๋น„์„ ํ˜• ์ตœ์ ํ™”์— ์„ฑ๊ณต์ ์œผ๋กœ ์ ์šฉํ•˜์—ฌ IPC ์‹œ๋ฎฌ๋ ˆ์ด์…˜์˜ ํšจ์œจ์„ฑ์„ ํฌ๊ฒŒ ํ–ฅ์ƒ์‹œ์ผฐ์Šต๋‹ˆ๋‹ค.
โ€ข
ํฌ์†Œ ์ž…๋ ฅ ์šฐ๋“œ๋ฒ„๋ฆฌ ์—…๋ฐ์ดํŠธ๋Š” ๊ธฐ์กด์˜ ๊ณ ๋น„์šฉ ์‚ฌ์ „์กฐ๊ฑด๊ธฐ ์žฌ๊ตฌ์ถ•์„ ๋Œ€์ฒดํ•˜์—ฌ ์‹ค์‹œ๊ฐ„์œผ๋กœ ๋ณ€ํ™”ํ•˜๋Š” ์ ‘์ด‰ ์ƒํ™ฉ์— ํšจ๊ณผ์ ์œผ๋กœ ๋Œ€์ฒ˜ํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
โ€ข
์ œ์•ˆ๋œ MAS-PNCG ๋ฐฉ๋ฒ•์€ ๊ธฐ์กด์˜ ์ตœ์ฒจ๋‹จ ์†”๋ฒ„๋“ค๋ณด๋‹ค ํ›จ์”ฌ ๋น ๋ฅธ ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ์†๋„๋ฅผ ๋ณด์—ฌ์ฃผ๋ฉฐ, ํŠนํžˆ ์ ‘์ด‰์ด ๋งŽ์€ ์–ด๋ ค์šด ์‹œ๋‚˜๋ฆฌ์˜ค์—์„œ ์„ฑ๋Šฅ์ด ๋‘๋“œ๋Ÿฌ์ง‘๋‹ˆ๋‹ค.
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ํ–ฅํ›„ ์—ฐ๊ตฌ์—์„œ๋Š” ๋” ๋ณต์žกํ•œ ๋ฌผ๋ฆฌ ํ˜„์ƒ(์˜ˆ: ๋งˆ์ฐฐ, ๋น„์„ ํ˜• ์žฌ๋ฃŒ)์— ๋Œ€ํ•œ MAS-PNCG์˜ ์ ์šฉ ๊ฐ€๋Šฅ์„ฑ์„ ํƒ์ƒ‰ํ•˜๊ฑฐ๋‚˜, ํ•˜๋“œ์›จ์–ด ๊ฐ€์†์„ ํ†ตํ•ด ๋”์šฑ ๋น ๋ฅธ ๊ณ„์‚ฐ์„ ๊ตฌํ˜„ํ•˜๋Š” ๋ฐฉ์•ˆ์„ ๊ณ ๋ คํ•  ์ˆ˜ ์žˆ์Šต๋‹ˆ๋‹ค.
๐Ÿ‘
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