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粒子法について その2
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touyou
May 17, 2018
Programming
1
90
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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Transcript
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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>
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=">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</latexit> <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>
όέοτߏ ཻࢠ๏ೖͦͷ̎ ɾҰఆͷେ͖͞ͷ όέοτʹ͚Δ ɾ֤όέοτʹ ௨͠൪߸Λ;Δ
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৽͍࣮͠ ཻࢠ๏ೖͦͷ̎ ཻࢠΛฒΔ ԾΛܭࢉ͢Δ ԾΛͬͯҠಈ͢Δ ඇѹॖ݅Λຬͨ͢Α͏ʹ ѹྗΛܭࢉ ҐஔͱΛ࠶ܭࢉ
৽͍࣮͠ ཻࢠ๏ೖͦͷ̎ ཻࢠΛฒΔ όέοτใΛߋ৽ ೪ੑ߲ॏྗ߲ͰԾͱԾҐஔ ࣮ࡍͷѹྗΛग़͢ ԾͷѹྗΛܭࢉ ࣮ࡍͷҐஔɾΛग़͢
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݁Ռ ཻࢠ๏ೖͦͷ̎ ӄղ๏ʜ࣮ߦ࣌ؒTFD ཻࢠεςοϓ γϛϡϨʔγϣϯͨ࣌ؒ͠TFD ཅղ๏ʜ࣮ߦ࣌ؒTFD ཻࢠεςοϓ γϛϡϨʔγϣϯͨ࣌ؒ͠TFD ཅղ๏ 0QFO.1
ʜ࣮ߦ࣌ؒTFD ཻࢠεςοϓ γϛϡϨʔγϣϯͨ࣌ؒ͠TFD
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