1、電路的計(jì)算機(jī)仿真,邱哲儒PB15000034,電磁學(xué)小論文演示文稿,目錄一.理論討論1.從最簡(jiǎn)單的情況開始2.對(duì)恒壓源的處理3.受控電源的處理4.非線性電路的迭代求解5.電路的時(shí)域動(dòng)態(tài)分析二.計(jì)算機(jī)實(shí)現(xiàn)1.編寫的程序XLWSpice2.應(yīng)用舉例i)包含二極管的算例ii)RC,RLC電路暫態(tài)過程的算例iii)大型電阻網(wǎng)絡(luò)的計(jì)算3.前景展望,1.最簡(jiǎn)單的情況：只有電流源與線性電阻,2.電壓源的處理,0.2000-0.200000001.000000-0.20000.4867-0.16670-0.0200-0.10000000-0.16670.166700000-1.0000000000001.00

2、000-0.0200000.0200000-1.00000-0.10000000.100001.000001.000000000000000001.0000000001.0000-1.000000000,等效電導(dǎo),等效電流源,在每次迭代中非線性器件可以等效為一個(gè)電流源并聯(lián)一個(gè)電阻,5.電路的時(shí)域動(dòng)態(tài)分析,1.編寫程序XLWSpice,XiaoLunWenSpice特點(diǎn)：使用C+語(yǔ)言代碼精簡(jiǎn),不含外部庫(kù)只有一千兩百余行使用高性能線性代數(shù)庫(kù)Eigen進(jìn)行稀疏矩陣的運(yùn)算通過PardisoSupport模塊調(diào)用IntelMKLPardisoLU進(jìn)行方程求解（兼顧Eigen的友好接口，MKL的優(yōu)秀性能）

3、,輸入為網(wǎng)表數(shù)據(jù)，詳情見源碼注釋輸出示例：,%NONLINEARDCANALYSIS%ABSOLUTECOVERGENCELIMIT:0.0001%RELATIVECOVERGENCELIMIT:0.001%HAVINGNODES:14%NONLINEARDCANALYSISITERATION0%NODEVOLTAGE1,12,0.1228173,0.5810274,0.2961565,0.2456346,0.4469267,0.3579628,0.3179299,0.40178910,0.37083911,0.3501912,0.38760113,0.37341414,0.361802%VO

4、LTAGESOURCESCURRENT0,-1.41897,VSRC1%STOPITERATIONCRITERIAMET,%NONLINEARDCANALYSIS%ABSOLUTECOVERGENCELIMIT:0.0001%RELATIVECOVERGENCELIMIT:0.001%HAVINGNODES:6%NONLINEARDCANALYSISITERATION0%NODEVOLTAGE1,102,17.33333,23.33334,23.33335,67.33336,12%VOLTAGESOURCESCURRENT0,1.46667,VSRC11,0.533333,VSRC2%STOP

5、ITERATIONCRITERIAMET,.DC1e-41e-3VSRC11010R125R236I401R5250R2610VSRC26012F05341,2.算例1:包含晶體二極管的簡(jiǎn)單電路,解得節(jié)點(diǎn)2的電壓,時(shí)間/s,絕對(duì)誤差/V,算例3:RLC電路的暫態(tài)過程,節(jié)點(diǎn)2電壓/V,電路處在欠阻尼狀態(tài),結(jié)果與理論值符合良好,0.1s步長(zhǎng)，求解100步,算例4：蔡氏電路,求解10s,步長(zhǎng)0.01s可以明顯看到蔡氏電路的混沌式的振蕩。有“雙渦旋”結(jié)構(gòu),算例5：運(yùn)用于大型電阻網(wǎng)格問題,對(duì)于大型規(guī)律性的電阻網(wǎng)絡(luò)，LU算法直接求解效果最佳。IntelMKL支持多核并行計(jì)算，大大提高求解性能，Pardis

6、oLU較Eigen內(nèi)置SparseLU至少快一倍。BiCGSTAB等迭代求解器，因Eigen庫(kù)的限制，矢量矩陣乘積無法并行化實(shí)驗(yàn)證明對(duì)于大型規(guī)律性的電阻網(wǎng)絡(luò)效果很不好，N=750時(shí)需要超過50s,用大型電阻網(wǎng)格問題的求解作為性能評(píng)價(jià),測(cè)試環(huán)境：Intel(R)64Compiler16.0.1.146關(guān)鍵選項(xiàng)/O3/QparallelEigen3.2.8IntelMKL11.3WindowsServer2012R2Intel(R)Core(TM)i5-5200UCPU2.20GHz8GRAM,總體性能令人滿意,直觀分析計(jì)算結(jié)果,電勢(shì)-節(jié)點(diǎn)位置圖（截取中心部分）,電勢(shì)-節(jié)點(diǎn)位置圖（橫斷面）,局部放

7、大,直觀分析計(jì)算結(jié)果,“等勢(shì)線”,可以明顯看出電流擴(kuò)散的各向異性沿00,11方向電阻較小,有四萬(wàn)節(jié)點(diǎn)，求解仍可以在0.5s內(nèi)完成,3.前景展望,獲取源碼和完整版演示文稿請(qǐng)?jiān)L問,參考文獻(xiàn)1KincaidDR,CheneyEW.Numericalanalysis:mathematicsofscientificcomputingM.AmericanMathematicalSoc.,2002.2邱關(guān)源,電路(第五版)M,高等教育出版社3VladimirescuA.TheSPICEBookM,1994.JohnWiley&Sons,NewYork,1994.4張運(yùn)華等,數(shù)值計(jì)算方法與算法(第二版)M,科學(xué)出版社5AtkinsonD,VanSteenwijkFJ.InfiniteresistivelatticesJ.AmericanJournalofPhysics,1999,67(6):486-492.6DenardoB,EarwoodJ,SazonovaV.ExperimentswithelectricalresistivenetworksJ.AmericanJournalofPhysics,1999,67(11):981-986.7CsertiJ.Applicationofthelat