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粒子法について その2

粒子法について その2

粒子法について その1の続編です。半陰解法から陽解法で変わる点、および並列化に役立つ手法を紹介しています。

touyou

May 17, 2018
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  1. φϏΤετʔΫεํఔࣜ ɾྲྀମͷӡಈํఔࣜ ɾV͕଎౓ɺH͕ॏྗՃ଎౓ ɾЛ͕ີ౓ɺӈลͷୈೋ߲͸೪ੑ߲ Du Dt = 1 ⇢0 rP

    + ⌫r2u + g <latexit sha1_base64="yKPKKX6ok3LUNzgZae4Payddraw=">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</latexit> <latexit sha1_base64="yKPKKX6ok3LUNzgZae4Payddraw=">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</latexit> <latexit sha1_base64="yKPKKX6ok3LUNzgZae4Payddraw=">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</latexit> <latexit sha1_base64="yKPKKX6ok3LUNzgZae4Payddraw=">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</latexit>
  2. ɾ৽͍͠ࢧ഑ํఔࣜ ɾD͸Ի଎ ཅղ๏ͷ֓ཁ ཻࢠ๏ೖ໳ͦͷ̎ @P @⇢ = c2 <latexit sha1_base64="qdR5EHiA5ZlZQedVOGBa2v7hgvk=">AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu</latexit>

    <latexit sha1_base64="qdR5EHiA5ZlZQedVOGBa2v7hgvk=">AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu</latexit> <latexit sha1_base64="qdR5EHiA5ZlZQedVOGBa2v7hgvk=">AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu</latexit> <latexit sha1_base64="qdR5EHiA5ZlZQedVOGBa2v7hgvk=">AAACHHicbVDLSgMxFM34rPVVdekmWARXZaYIuhGKblxWsA/ojCWTZtrQPIYkI5RhPsCf8Bfc6t6duBXc+iVm2kG09UDgcM65uckJY0a1cd1PZ2l5ZXVtvbRR3tza3tmt7O23tUwUJi0smVTdEGnCqCAtQw0j3VgRxENGOuH4Kvc790RpKsWtmcQk4GgoaEQxMlbqV6p+pBBO/RgpQxGDzeyH+2okswt8V7cpt+ZOAReJV5AqKNDsV778gcQJJ8JghrTueW5sgjS/FjOSlf1EkxjhMRqSnqUCcaKDdPqZDB5bZQAjqewRBk7V3xMp4lpPeGiTHJmRnvdy8V8v5HObTXQepFTEiSECzxZHCYNGwrwpOKCKYMMmliCsqH07xCNk2zK2z7ItxZuvYJG06zXPrXk3p9XGZVFPCRyCI3ACPHAGGuAaNEELYPAAnsAzeHEenVfnzXmfRZecYuYA/IHz8Q1q7aJu</latexit>
  3. มԽ͢Δͱ͜Ζ ཻࢠ๏ೖ໳ͦͷ̎ 1 ⇢0 2d 0n0 X j6=i Pk+1 j

    Pk+1 i w(|r⇤ j r⇤ i |) = 1 t2 n⇤ i n0 n0 <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit> <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit> <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit> <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit>
  4. มԽ͢Δͱ͜Ζ ཻࢠ๏ೖ໳ͦͷ̎ 1 ⇢0 2d 0n0 X j6=i Pk+1 j

    Pk+1 i w(|r⇤ j r⇤ i |) = 1 t2 n⇤ i n0 n0 <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit> <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit> <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit> <latexit sha1_base64="KsBHfA3vE/j+/XdkySXMek/+q74=">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</latexit> P⇤ = c2⇢ n⇤ n0 n0 Pk+1 = c2⇢ nk+1 n0 n0 <latexit sha1_base64="mjElurW5PyLGDXCVu35LEx2uPNk=">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</latexit> <latexit sha1_base64="mjElurW5PyLGDXCVu35LEx2uPNk=">AAACQHicbVDNS8MwHE3n16xfU49eikOQiaMdgl6EoQc9VnAfsLYjzdItLE1Lkgqj7E/yn/Bf8CToxZM38erJtBuo1QcJj/fej1/y/JgSIU3zSSstLC4tr5RX9bX1jc2tyvZOW0QJR7iFIhrxrg8FpoThliSS4m7MMQx9ijv++DLzO3eYCxKxWzmJsRvCISMBQVAqqV+5sr3aOfIaDh9FTsAhSplXO2aeOU2zy3F020vHR9a0GMrF72C/UjXrZg7jL7HmpArmsPuVV2cQoSTETCIKhehZZizdFHJJEMVT3UkEjiEawyHuKcpgiIWb5h+eGgdKGRhBxNVh0sjVnxMpDIWYhL5KhlCORNHLxH89PyxslsGZmxIWJxIzNFscJNSQkZG1aQwIx0jSiSIQcaLebqARVA1J1bmuSrGKFfwl7UbdMuvWzUm1eTGvpwz2wD44BBY4BU1wDWzQAgjcg0fwDF60B+1Ne9c+ZtGSNp/ZBb+gfX4BZaevYw==</latexit> <latexit sha1_base64="mjElurW5PyLGDXCVu35LEx2uPNk=">AAACQHicbVDNS8MwHE3n16xfU49eikOQiaMdgl6EoQc9VnAfsLYjzdItLE1Lkgqj7E/yn/Bf8CToxZM38erJtBuo1QcJj/fej1/y/JgSIU3zSSstLC4tr5RX9bX1jc2tyvZOW0QJR7iFIhrxrg8FpoThliSS4m7MMQx9ijv++DLzO3eYCxKxWzmJsRvCISMBQVAqqV+5sr3aOfIaDh9FTsAhSplXO2aeOU2zy3F020vHR9a0GMrF72C/UjXrZg7jL7HmpArmsPuVV2cQoSTETCIKhehZZizdFHJJEMVT3UkEjiEawyHuKcpgiIWb5h+eGgdKGRhBxNVh0sjVnxMpDIWYhL5KhlCORNHLxH89PyxslsGZmxIWJxIzNFscJNSQkZG1aQwIx0jSiSIQcaLebqARVA1J1bmuSrGKFfwl7UbdMuvWzUm1eTGvpwz2wD44BBY4BU1wDWzQAgjcg0fwDF60B+1Ne9c+ZtGSNp/ZBb+gfX4BZaevYw==</latexit> <latexit sha1_base64="mjElurW5PyLGDXCVu35LEx2uPNk=">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</latexit>