{"id":207,"date":"2019-09-03T13:37:20","date_gmt":"2019-09-03T04:37:20","guid":{"rendered":"https:\/\/www.ssil.co.jp\/product\/EMSolution2\/?post_type=case&p=207"},"modified":"2024-12-16T09:29:31","modified_gmt":"2024-12-16T00:29:31","slug":"coil_inductance_in_infinite_boundary_element","status":"publish","type":"case","link":"https:\/\/www.ssil.co.jp\/product\/EMSolution\/case\/coil_inductance_in_infinite_boundary_element\/","title":{"rendered":"\u7121\u9650\u5883\u754c\u8981\u7d20\u306b\u3088\u308b\u30b3\u30a4\u30eb\u30a4\u30f3\u30c0\u30af\u30bf\u30f3\u30b9"},"content":{"rendered":"

\u6982\u8981<\/h3>\n

\u65e2\u306bEMSolution\u306b\u304a\u3051\u308b\u7121\u9650\u5883\u754c\u8981\u7d20\u306e\u53d6\u308a\u7d44\u307f\u306f"\u7121\u9650\u5883\u754c\u8981\u7d20\u306e\u9069\u7528"<\/font><\/a>\uff0c"\u5883\u754c\u6761\u4ef6\u3068\u7121\u9650\u8981\u7d20"<\/font><\/a>\u3067\u8ff0\u3079\u3066\u3044\u307e\u3059\u3002\u7121\u9650\u5883\u754c\u8981\u7d20\u306f\u89e3\u6790\u9818\u57df\u5883\u754c\u306b\u7121\u9650\u9060\u306b\u9054\u3059\u308b\u6709\u9650\u8981\u7d20\u3092\u52a0\u3048\u305f\u3053\u3068\u3068\u7b49\u4fa1\u3067\uff0c\u6709\u9650\u8981\u7d20\u6cd5\u3067\u958b\u9818\u57df\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002\u901a\u5e38\uff0c\u6709\u9650\u8981\u7d20\u6cd5\u306e\u89e3\u6790\u9818\u57df\u306e\u5883\u754c\u306e\u5f71\u97ff\u3092\u7121\u304f\u3059\u305f\u3081\u306b\u306f\uff0c\u304b\u306a\u308a\u5e83\u3044\u7a7a\u6c17\u306e\u89e3\u6790\u9818\u57df\u3092\u8a2d\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\uff0c\u7121\u9650\u5883\u754c\u8981\u7d20\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\uff0c\u7a7a\u6c17\u306e\u89e3\u6790\u9818\u57df\u3092\u524a\u6e1b\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3068\u306a\u308a\uff0c\u30e1\u30c3\u30b7\u30e5\u5206\u5272\u3082\u5bb9\u6613\u306b\u306a\u308b\u3060\u3051\u3067\u306a\u304f\u8a08\u7b97\u6642\u9593\u3092\u77ed\u7e2e\u3059\u308b\u3053\u3068\u304c\u671f\u5f85\u3067\u304d\u307e\u3059\u3002 <\/p>\n

\u89e3\u8aac<\/h3>\n

\u672c\u624b\u6cd5\u306f\u8ef8\u5bfe\u79f0\u4e09\u6b21\u5143\u304a\u3088\u3073\u4e09\u6b21\u5143\u306e\u89e3\u6790\u3067\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5f93\u6765\uff0c\u8ef8\u5bfe\u79f0\u4e09\u6b21\u5143\u3067\u306fICCG\u6cd5\u306e\u53ce\u675f\u6027\u306f\u554f\u984c\u306a\u304f\u975e\u5e38\u306b\u6709\u52b9\u306a\u65b9\u6cd5\u3067\u3059\u304c\uff0c\u4e09\u6b21\u5143\u89e3\u6790\u3067\u306f\u53ce\u675f\u6027\u304c\u554f\u984c\u3068\u306a\u3063\u3066\u304a\u308a\u307e\u3057\u305f\u304c\uff0c\u3053\u306e\u5ea6\u9ad8\u901f\u5316\u306b\u6210\u529f\u3057\uff0c\u5b9f\u52d9\u30ec\u30d9\u30eb\u306e\u8a08\u7b97\u6642\u9593\u3068\u306a\u308a\u307e\u3057\u305f\u3002 <\/p>\n

\u3053\u3053\u3067\u306f\uff0c\u4e09\u6b21\u5143\u89e3\u6790\u306b\u304a\u3051\u308b\u7121\u9650\u5883\u754c\u8981\u7d20\u3092\u9069\u7528\u3057\uff0cFig.1\u3067\u793a\u3055\u308c\u308b\u96fb\u6c17\u5b66\u4f1a\u691c\u8a3c\u7528\u30b3\u30a4\u30eb\u306e\u30a4\u30f3\u30c0\u30af\u30bf\u30f3\u30b9\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u30b3\u30a4\u30eb\u306f\u7a7a\u5fc3\u3068\u3057\uff0c\u5bfe\u79f0\u6027\u3088\u308a\u5168\u4f53\u306e1\/8\u9818\u57df\u306e\u9759\u78c1\u5834\u89e3\u6790\u3092\u884c\u3044\u307e\u3059\u3002\u30b3\u30a4\u30eb\u306fSDEFCOIL\u3068\u3057\u3066\u5b9a\u7fa9\u3057\uff0c\u30a4\u30f3\u30c0\u30af\u30bf\u30f3\u30b9\u306f\uff0cLI=\u222bA\u30fbJdV \u306b\u3088\u308a\u6c42\u3081\u3089\u308c\u307e\u3059\u3002 <\/p>\n

\n
\n \"\"<\/a><\/p>\n

Fig.1\u3000\u96fb\u6c17\u5b66\u4f1a\u691c\u8a3c\u7528\u30b3\u30a4\u30eb<\/p>\n<\/p><\/div>\n<\/div>\n

\u5bfe\u79f0\u5883\u754c\u4ee5\u5916\u306e\u9060\u65b9\u5883\u754c\u306b\u7121\u9650\u5883\u754c\u8981\u7d20\u3092\u9069\u7528\u3057\uff0c\u30b3\u30a4\u30eb\u5916\u5074\u306b\u7a7a\u6c17\u9818\u57df\u3092\u53d6\u3089\u306a\u3044\u5834\u5408\uff081\u500d\u9818\u57df\uff09\uff0c\u4e09\u6b21\u5143\u306e\u5404\u65b9\u5411\u306b\u305d\u306e2\u500d\u304a\u3088\u30734\u500d\u306e\u7a7a\u6c17\u9818\u57df\u3067\u89e3\u6790\u3092\u884c\u3044\u307e\u3057\u305f\u3002\u5916\u90e8\u9818\u57df\u78c1\u5834\u306e\u7121\u9650\u5883\u754c\u8981\u7d20\u306e\u5c55\u958b\u6b21\u6570\uff08\u4ee5\u4e0b\uff0c\u30aa\u30fc\u30c0\u30fc\u3068\u547c\u3076\uff09\u306f\uff0c\u591a\u304f\u53d6\u308b\u306b\u5f93\u3044\u7cbe\u5ea6\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002 Fig.2\u3067\u898b\u3089\u308c\u307e\u3059\u3088\u3046\u306b\uff0c\u89e3\u6790\u9818\u57df\u5185\u306e\u78c1\u5834\u306f\u7a7a\u6c17\u9818\u57df\u306e\u5927\u304d\u3055\u306b\u304b\u304b\u308f\u3089\u305a\uff0c\u307b\u307c\u4e00\u81f4\u3057\u305f\u7d50\u679c\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002Fig.2(a)\u306e1\u500d\u9818\u57df\u306e\u3088\u3046\u306b\uff0c\u30b3\u30a4\u30eb\u3068\u305d\u306e\u5185\u90e8\u306e\u7a7a\u6c17\u3060\u3051\u3067\u30b3\u30a4\u30eb\u5916\u90e8\u306e\u7a7a\u6c17\u9818\u57df\u304c\u306a\u304f\u3066\u3082\uff0c\u7cbe\u5ea6\u3088\u304f\u89e3\u6790\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>\n

\n
\n \"\"<\/a><\/p>\n

(1)\u30001\u500d\u9818\u57df(order 3)<\/p>\n<\/p><\/div>\n

\n \"\"<\/a><\/p>\n

(2)\u30002\u500d\u9818\u57df(order 3)<\/p>\n<\/p><\/div>\n

\n \"\"<\/a><\/p>\n

(3)\u30004\u500d\u9818\u57df(order 2)<\/p>\n<\/p><\/div>\n

Fig.2\u3000\u89e3\u6790\u9818\u57df\u3068\u78c1\u675f\u5bc6\u5ea6\u5f37\u5ea6\u5206\u5e03<\/p>\n<\/div>\n

Fig.3\u306b\u793a\u3059\u3088\u3046\u306b\uff0c\u8a08\u7b97\u3055\u308c\u305f\u30a4\u30f3\u30c0\u30af\u30bf\u30f3\u30b9\u306e\u7cbe\u5ea6\u306f\u89e3\u6790\u9818\u57df\u306e\u5927\u304d\u3055\u3068\u7121\u9650\u5883\u754c\u8981\u7d20\u306e\u30aa\u30fc\u30c0\u30fc\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u89e3\u6790\u9818\u57df\u3092\u5927\u304d\u304f\uff0c\u307e\u305f\u30aa\u30fc\u30c0\u30fc\u3092\u9ad8\u304f\u3059\u308b\u306b\u5f93\u3044\uff0c\u30a4\u30f3\u30c0\u30af\u30bf\u30f3\u30b9\u304c\u4e00\u5b9a\u5024\u306b\u53ce\u675f\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u4e00\u822c\u306b\uff0c\u771f\u306e\u30a4\u30f3\u30c0\u30af\u30bf\u30f3\u30b9\u5024\u306f\u5883\u754c\u6761\u4ef6\u3092Bn=0\u3068Ht=0\u3067\u89e3\u3044\u305f\u4e2d\u9593\u306b\u306a\u308a\u307e\u3059\u304c\uff0c\u4eca\u56de\u3082\uff0c\u305d\u306e\u3088\u3046\u306a\u50be\u5411\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u5fc5\u8981\u3068\u3059\u308b\u89e3\u6790\u7cbe\u5ea6\u306b\u3088\u308a\u307e\u3059\u304c\uff0c1\u500d\u9818\u57df\u306e\u89e3\u6790\u3067\u306f4\u6b21\u306e\u30aa\u30fc\u30c0\u30fc\u306e\u8a08\u7b97\u304c\u5fc5\u8981\u3067\u3059\u304c\uff0c4\u500d\u9818\u57df\u306e\u89e3\u6790\u3067\u306f1\u6b21\u306e\u30aa\u30fc\u30c0\u30fc\u3067\u5341\u5206\u306a\u7cbe\u5ea6\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002Table I\u306b\uff0c\u89e3\u6790\u8af8\u5143\u3092\u307e\u3068\u3081\u307e\u3059\u3002
\n\u6b21\u306b\u8a08\u7b97\u6642\u9593\u306e\u6bd4\u8f03\u3092\u884c\u3044\u307e\u3059\u3002Fig.4\u306b\u793a\u3059\u3088\u3046\u306b\uff0c\u540c\u3058\u89e3\u6790\u9818\u57df\u3067\u306f\uff0c\u7121\u9650\u8981\u7d20\u3092\u4f7f\u7528\u3059\u308b\u3068\u8a08\u7b97\u6642\u9593\u304c\u5897\u52a0\u3057\u307e\u3059\u3002\u5f93\u6765\u306f\u3001\u7279\u306b\u30aa\u30fc\u30c0\u30fc\u3092\u9ad8\u304f\u3057\u307e\u3059\u3068\uff0c\u6025\u6fc0\u306b\u305d\u306e\u8a08\u7b97\u6642\u9593\u304c\u5897\u5927\u3059\u308b\u554f\u984c\u304c\u3042\u308a\u307e\u3057\u305f\u304c\u3001\u9ad8\u901f\u5316\u306b\u3088\u308a\u8a08\u7b97\u6642\u9593\u306e\u77ed\u7e2e\u306b\u6210\u529f\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u793a\u305b\u3066\u3044\u308b\u304b\u3068\u601d\u3044\u307e\u3059\u3002\u5165\u529b\u306f\u5f93\u6765\u3068\u5909\u308f\u308a\u307e\u305b\u3093\u3002\u662f\u975e\u304a\u4f7f\u3044\u9802\u3051\u308c\u3070\u3068\u601d\u3044\u307e\u3059\u3002 <\/p>\n

\n
\n \"\"<\/a><\/p>\n

Fig.3\u3000\u89e3\u6790\u9818\u57df\u306e\u5927\u304d\u3055\u3068
\u7121\u9650\u5883\u754c\u8981\u7d20\u30aa\u30fc\u30c0\u30fc\u306b\u3088\u308b
\u30a4\u30f3\u30c0\u30af\u30bf\u30f3\u30b9\u306e\u6bd4\u8f03<\/p>\n<\/p><\/div>\n

\n \"\"<\/a><\/p>\n

Fig.4\u3000\u89e3\u6790\u9818\u57df\u306e\u5927\u304d\u3055\u3068
\u7121\u9650\u5883\u754c\u8981\u7d20\u30aa\u30fc\u30c0\u30fc\u306b\u3088\u308b
\u8a08\u7b97\u6642\u9593\u306e\u6bd4\u8f03<\/p>\n<\/p><\/div>\n<\/div>\n

\uff08\uff11\uff091\u500d\u9818\u57df<\/h2>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
<\/td>Ht=0<\/th>Bn=0<\/th>\u7121\u9650\u8981\u7d20<\/th>\n<\/tr>\n<\/thead>\n
Oder<\/td>0<\/td>0<\/td>1<\/td>2<\/td>3<\/td>4<\/td>\n<\/tr>\n
Number of elements<\/td>30,400<\/td>\n<\/tr>\n
Number of nodes<\/td>33,201<\/td>\n<\/tr>\n
Number of unknowns<\/td>93,420<\/td>88,180<\/td>96,020<\/td>103,860<\/td>111,700<\/td>119,540<\/td>\n<\/tr>\n
Number of non-zeros<\/td>1,510,993<\/td>1,424,411<\/td>1,554,407 <\/td>1,805,615<\/td>2,178,035<\/td>2,671,667<\/td>\n<\/tr>\n
ICCG Itarations
error <$10^{-8}$<\/td>		81 \/ 138*<\/td>81 \/ 146*<\/td>142 \/ 203*<\/td>204 \/ 817*<\/td>235 \/ 3,838*<\/td>261 \/ 16,356*<\/td>\n<\/tr>\n
CPU Times (s) <\/td>3.2 \/ 3.7* <\/td>3.2 \/ 4.2* <\/td>5.0 \/ 5.8<\/td>7.1 \/ 32.3* <\/td>9.4 \/ 195.5* <\/td>12.2 \/ 1,001.5* <\/td>\n<\/tr>\n
Inductance (H) <\/td>3.38133E-03<\/td>3.04443E-04<\/td>1.50634E-03<\/td>1.67678E-03<\/td>1.69503E-03<\/td>1.69917E-03<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n*\u7121\u9650\u8981\u7d20\u9ad8\u901f\u5316\u306b\u3088\u308b\u7d50\u679c\uff0f\u5f93\u6765\u306e\u7121\u9650\u8981\u7d20\u306b\u3088\u308b\u7d50\u679c <\/p>\n

\uff08\uff12\uff09\uff12\u500d\u9818\u57df<\/h2>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
<\/td>Ht=0<\/th>Bn=0<\/th>\u7121\u9650\u8981\u7d20<\/th>\n<\/tr>\n<\/thead>\n
Order<\/td>0<\/td>0<\/td>1<\/td>2<\/td>3<\/td>4<\/td>\n<\/tr>\n
Number of elements<\/td>67,648<\/td>\n<\/tr>\n
Number of nodes<\/td>72,297<\/td>\n<\/tr>\n
Number of unknowns<\/td>205,724<\/td>197,820<\/td>209,644<\/td>221,468<\/td>233,292<\/td>245,116 <\/td>\n<\/tr>\n
Number of non-zeros<\/td>3,370,313 <\/td>3,238,899 <\/td>3,435,999 <\/td>381,039<\/td>4,379,019<\/td>5,124,939 <\/td>\n<\/tr>\n
ICCG Itarations
error < $10^{-8}$<\/td>		138<\/td>146<\/td>204 \/ 203*<\/td>249 \/ 817*<\/td>277 \/ 3,838*<\/td>297 \/ 16,356*<\/td>\n<\/tr>\n
CPU Times (s) <\/td>10.3 \/ 12.4* <\/td>10.5 \/ 12.8* <\/td>14.5 \/ 20.2* <\/td>18.2 \/ 61.7* <\/td>22.3 \/ 321.7* <\/td>27.2 \/ 1,518.8* <\/td>\n<\/tr>\n
Inductance (H) <\/td>2.06976E-03<\/td>1.42398E-03<\/td>1.69477E-03<\/td>1.70070E-03<\/td>1.70081E-03<\/td>1.70082E-03<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n*\u7121\u9650\u8981\u7d20\u9ad8\u901f\u5316\u306b\u3088\u308b\u7d50\u679c\uff0f\u5f93\u6765\u306e\u7121\u9650\u8981\u7d20\u306b\u3088\u308b\u7d50\u679c <\/p>\n

\uff08\uff13\uff09\uff14\u500d\u9818\u57df<\/h2>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
<\/td>Ht=0<\/th>Bn=0<\/th>\u7121\u9650\u8981\u7d20<\/th>\n<\/tr>\n<\/thead>\n
Order<\/td>0<\/td>0<\/td>1<\/td>2<\/td>\n<\/tr>\n
Number of elements<\/td>103,104<\/td>\n<\/tr>\n
Number of nodes<\/td>109,113<\/td>\n<\/tr>\n
Number of unknowns<\/td>311,828 <\/td>302,148<\/td>316,628<\/td>331,108<\/td>\n<\/tr>\n
Number of non-zeros<\/td>5,136,633<\/td>4,975,331<\/td>5,217,167<\/td>5,683,095<\/td>\n<\/tr>\n
ICCG Itarations
error < $10^{-8}$<\/td>		218<\/td>208<\/td>267<\/td>304 \/ 1,004*<\/td>\n<\/tr>\n
CPU Times (s) <\/td>22.6 \/ 24.7* <\/td>21.0 \/ 23.6* <\/td>26.9 \/ 29.3* <\/td>32.4 \/ 107.8* <\/td>\n<\/tr>\n
Inductance (H) <\/td>1.75995E-03<\/td>1.65485E-03<\/td>1.70062E-03<\/td>1.70069E-03<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
\n*\u7121\u9650\u8981\u7d20\u9ad8\u901f\u5316\u306b\u3088\u308b\u7d50\u679c\uff0f\u5f93\u6765\u306e\u7121\u9650\u8981\u7d20\u306b\u3088\u308b\u7d50\u679c <\/p>\n

<\/p>\n

\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9<\/h3>\n

1\u500d\u9818\u57df