comsol實(shí)例學(xué)習(xí)muchong com求解器

1、 Copyright 2016 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property oftheir respective owners. See.p = 2 Nk = 4 N/mu?p = 2 Nk = 4 N/mu?f (u)usolution= 0.5f (u) = p k u = 0f (u) = 2 - 4 u = 0uf (u) = p - k uusolutio

2、n= 0.5uu0=0f (u)f (u) = p k uup，kuf (u) = p(u) k(u)u mu2 uk = exp(u) N/mp = 2 Nuf (u) = 2 exp(u)uuf (u) = 2 exp(u)uuu0=0iuif(ui)f(ui)00.0002.0001.000u1= 2uiuif(ui)f(ui)00.0002.0001.00012.000-12.77-22.167u1= 1.424uiuif(ui)f(ui)00.0002.0001.00012.000-12.77-22.16721.424-3.915-10.069u1= 1.035uiuif(ui)f(

3、ui)00.0002.0001.00012.000-12.77-22.16721.424-3.915-10.06931.035-0.914-5.729uiuif(ui)f(ui)00.0002.0001.00012.000-12.77-22.16721.424-3.915-10.06931.035-0.914-5.72940.876-0.104-4.505uiuif(ui)f(ui)00.0002.0001.00012.000-12.77-22.16721.424-3.915-10.06931.035-0.914-5.72940.876-0.104-4.50550.8530.002-4.348

4、60.8520.001-4.342ur(u)iuif(ui)|ui-1 - ui|f(ui-1) - f(ui)|00.0002.00012.000-12.772.00010.7721.424-3.9150.5768.85531.035-0.9140.3893.00140.876-0.1040.1590.81050.8530.0020.0230.10260.8520.0010.0010.001f(u0)uu0=0if: |f(u)| |f(u )|i+1if(u1)f(u0)uu0=0if: |f(u)| |f(u )|i+1ifind: u = ui+1 uif(u1)f(u0)uu0=0i

5、f: |f(u)| |f(u )|i+1ifind: u = ui+1 ui pick: 0 |f(u )|i+1if(u + u )find: u = ui+1 ui pick: 0 1 find: |f(ui + u)| repeat0- ui| 縮放因子 相對容差|ui-1Solutionpukpf (u) = 0.05 exp( u )uf (u) = 0.05 exp( u )uf (u) = 0.50 exp( u )uf (u) = 0.05 exp( u )uf (u) = 0.50 exp( u )uf (u) = 1.00 exp( u )uf (u) = 0.05 exp

6、( u )uf (u) = 0.50 exp( u )uf (u) = 1.00 exp( u )uf (u) = 2.00 exp( u )uu (p)pp0p1p2p3u (p)pp0p1p2p3p3p3puk(u)k (u)u (p)p4p3p1p2upf (u) = 2 exp(u)ukNL= exp(u)u0kLIN= exp(u0=0)k() = (1-)kLIN+kNLu0f (u) = 2 - k() u: 0 1f =2 k(=0.0)u = 2 - uf =2 k(=0.0)u f =2 k(=0.5)u f =2 k(=0.0)u f =2 k(=0.5)u f =2 k

7、(=1.0)up = 2 Nku?k = 1.5k (u)k = 1k = 0.5u1.92.1k = 1.5k (u)k = 1k = 0.5u2.11.9T=0Q=100W(1+T/20K)W/(m*K)k1W/(m*K)0.1+exp(-(T/25K)2)W/(m*K)TErroru(x)xabu(x)xabu(x)xabu(x)xabu(x)xabMore Elements：收斂速率強(qiáng)烈依賴于階次、類型，以及單元分布，這種收斂速率對不同的問題也完全不同。Solution10010210410610010-210-410-6 Copyright 2016 COMSOL. Any of t

8、he images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property oftheir respective owners. See.k1 = 3 N/mp = 1 Nk = 2 N/mk3 = 2 N/m2u1u2k1u2k3(u1-u2)k2u1pk3(u2-u1)f (u1) = k2u1 k3 (u1 u2)f (u2) = k1u2 k3 (u2 u1) + pf (u1) = k2u1 k3 (u1 u2)f (

9、u2) = k1u2 k3 (u2 u1) + pk + k3- k3u0f (u) =21- p- kk + k3 u2 31f(u)=Ku-busolution=K-1br(u) = f(u) f (u)u2u1f(u0) = Ku0-b f(u0) = Ku0 = 0usolution=K-1bu2u1f(u0) = Ku0-b f(u0) = Ku0 = 0u2u1Memory= A dof2 + B dof + (1GB) Copyright 2016 COMSOL. Any of the images, text, and equations here may be copied

10、and modified for your own internal use. All trademarks are the property oftheir respective owners. See.Start with uV,0 & uT,0fV (uV) = KV(uT,0)uV - bVfT (uT,uV) = KT(uT,0)uT bT (uV)uV,0 & uT,0fV (uV) = KV(uT) uV - bVfT (uT,uV) = KT(uT)uT bT (uV)uV,0 & uT,0fV (uV) = KV(uT) uV - bVfT (uT,uV) = KT(uT)uT bT (uV)uV,i , uT,i初始化:uV,i+1= uV,i - KV(uT,i, uV,i)-1fV(uT,i, uV,i)求解:uT,i+1= uT,i - KT(uT,i, uV,i+1)-1fT(uT,i, uV,i+1 )求解:i = i+1迭代:ui ui-1 & fi fi-1 容差滿足條件就結(jié)束:fT (uT) = KTuT - bT (uV)fV (uV) = KVuV - bVfV (uV , uT )uV KVuV 0b