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annotate +sbp/+implementations/d2_10.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents f7ac3cd6eeaa
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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6009f2712d13 Moved and renamned all implementations.
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diff changeset
1 function [H, HI, D1, D2, e_1, e_m, M, Q, S_1, S_m] = d2_10(m,h)
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2
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3 BP = 11;
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4 if(m<2*BP)
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5 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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6 end
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7
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8 H_U = [0.5261271563e10 / 0.18289152000e11 0 0 0 0 0 0 0 0 0 0; 0 0.2881040311e10 / 0.1828915200e10 0 0 0 0 0 0 0 0 0; 0 0 0.52175551e8 / 0.406425600e9 0 0 0 0 0 0 0 0; 0 0 0 0.11662993e8 / 0.6096384e7 0 0 0 0 0 0 0; 0 0 0 0 0.50124587e8 / 0.87091200e8 0 0 0 0 0 0; 0 0 0 0 0 0.50124587e8 / 0.72576000e8 0 0 0 0 0; 0 0 0 0 0 0 0.148333439e9 / 0.87091200e8 0 0 0 0; 0 0 0 0 0 0 0 0.63867949e8 / 0.152409600e9 0 0 0; 0 0 0 0 0 0 0 0 0.20608675e8 / 0.16257024e8 0 0; 0 0 0 0 0 0 0 0 0 0.1704508063e10 / 0.1828915200e10 0; 0 0 0 0 0 0 0 0 0 0 0.18425967263e11 / 0.18289152000e11;];
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9
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10 H=speye(m);
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11 H(1:11,1:11)=H_U;
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12 H(m-10:m,m-10:m)=rot90( H_U(1:11,1:11) ,2 );
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13 H=H*h;
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14 HI=inv(H);
6009f2712d13 Moved and renamned all implementations.
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15
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16 % Q=-(-1/1260*diag(ones(m-5,1),5)+5/504*diag(ones(m-4,1),4)-5/84*diag(ones(m-3,1),3)+5/21*diag(ones(m-2,1),2)-5/6*diag(ones(m-1,1),1)+5/6*diag(ones(m-1,1),-1)-5/21*diag(ones(m-2,1),-2)+5/84*diag(ones(m-3,1),-3)-5/504*diag(ones(m-4,1),-4)+1/1260*diag(ones(m-5,1),-5));
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17
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18 diags = -5:5;
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19 stencil = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
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20 Q = stripeMatrix(stencil, diags, m);
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23
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24 Q_U = [-0.1e1 / 0.2e1 0.2300876759589119e16 / 0.3395198177280000e16 -0.99808615498093e14 / 0.2263465451520000e16 -0.34957747037683e14 / 0.212199886080000e15 -0.709586095717e12 / 0.13473008640000e14 0.325330433051e12 / 0.6218311680000e13 0.27953548723573e14 / 0.485028311040000e15 0.2690678501e10 / 0.412439040000e12 -0.2397491025029e13 / 0.70733295360000e14 -0.9959492094287e13 / 0.1131732725760000e16 0.5242772857661e13 / 0.522338181120000e15; -0.2300876759589119e16 / 0.3395198177280000e16 0 0.3103439505511e13 / 0.16643128320000e14 0.2700334568377e13 / 0.5052378240000e13 0.50587599589937e14 / 0.242514155520000e15 -0.5570893587157e13 / 0.40419025920000e14 -0.1496329934863e13 / 0.8083805184000e13 -0.322512443237e12 / 0.12482346240000e14 0.2275340833763e13 / 0.23096586240000e14 0.22922115021893e14 / 0.848799544320000e15 -0.143e3 / 0.5000e4; 0.99808615498093e14 / 0.2263465451520000e16 -0.3103439505511e13 / 0.16643128320000e14 0 0.15053664233879e14 / 0.40419025920000e14 -0.9306441440587e13 / 0.32335220736000e14 -0.945459729233e12 / 0.13473008640000e14 0.956829267413e12 / 0.5774146560000e13 0.446866085903e12 / 0.56586636288000e14 -0.41109372242993e14 / 0.754488483840000e15 0.1e1 / 0.500e3 0.17e2 / 0.2500e4; 0.34957747037683e14 / 0.212199886080000e15 -0.2700334568377e13 / 0.5052378240000e13 -0.15053664233879e14 / 0.40419025920000e14 0 0.3899174751943e13 / 0.10104756480000e14 0.4691717443831e13 / 0.10104756480000e14 -0.58571891887e11 / 0.396264960000e12 0.100791910589e12 / 0.1040195520000e13 -0.425149181e9 / 0.29719872000e11 -0.2376515922259e13 / 0.30314269440000e14 0.36894656431e11 / 0.1036385280000e13; 0.709586095717e12 / 0.13473008640000e14 -0.50587599589937e14 / 0.242514155520000e15 0.9306441440587e13 / 0.32335220736000e14 -0.3899174751943e13 / 0.10104756480000e14 0 -0.4552305973e10 / 0.444165120000e12 0.4984940784247e13 / 0.11548293120000e14 -0.19410791e8 / 0.146764800e9 -0.2912773695913e13 / 0.40419025920000e14 0.127067639161e12 / 0.3233522073600e13 -0.89277540287e11 / 0.37309870080000e14; -0.325330433051e12 / 0.6218311680000e13 0.5570893587157e13 / 0.40419025920000e14 0.945459729233e12 / 0.13473008640000e14 -0.4691717443831e13 / 0.10104756480000e14 0.4552305973e10 / 0.444165120000e12 0 0.31722122083e11 / 0.84913920000e11 -0.887187251021e12 / 0.10104756480000e14 -0.1661755478749e13 / 0.26946017280000e14 0.1505713246249e13 / 0.13473008640000e14 -0.38859042469e11 / 0.1036385280000e13; -0.27953548723573e14 / 0.485028311040000e15 0.1496329934863e13 / 0.8083805184000e13 -0.956829267413e12 / 0.5774146560000e13 0.58571891887e11 / 0.396264960000e12 -0.4984940784247e13 / 0.11548293120000e14 -0.31722122083e11 / 0.84913920000e11 0 0.9357094407023e13 / 0.20209512960000e14 0.52602356173249e14 / 0.161676103680000e15 -0.1435252677707e13 / 0.17322439680000e14 -0.33048158431e11 / 0.3109155840000e13; -0.2690678501e10 / 0.412439040000e12 0.322512443237e12 / 0.12482346240000e14 -0.446866085903e12 / 0.56586636288000e14 -0.100791910589e12 / 0.1040195520000e13 0.19410791e8 / 0.146764800e9 0.887187251021e12 / 0.10104756480000e14 -0.9357094407023e13 / 0.20209512960000e14 0 0.70089734285659e14 / 0.141466590720000e15 -0.105938137621e12 / 0.471555302400e12 0.4358988450443e13 / 0.65292272640000e14; 0.2397491025029e13 / 0.70733295360000e14 -0.2275340833763e13 / 0.23096586240000e14 0.41109372242993e14 / 0.754488483840000e15 0.425149181e9 / 0.29719872000e11 0.2912773695913e13 / 0.40419025920000e14 0.1661755478749e13 / 0.26946017280000e14 -0.52602356173249e14 / 0.161676103680000e15 -0.70089734285659e14 / 0.141466590720000e15 0 0.314274398580227e15 / 0.377244241920000e15 -0.97822819709e11 / 0.487710720000e12; 0.9959492094287e13 / 0.1131732725760000e16 -0.22922115021893e14 / 0.848799544320000e15 -0.1e1 / 0.500e3 0.2376515922259e13 / 0.30314269440000e14 -0.127067639161e12 / 0.3233522073600e13 -0.1505713246249e13 / 0.13473008640000e14 0.1435252677707e13 / 0.17322439680000e14 0.105938137621e12 / 0.471555302400e12 -0.314274398580227e15 / 0.377244241920000e15 0 0.7519148725913e13 / 0.9327467520000e13; -0.5242772857661e13 / 0.522338181120000e15 0.143e3 / 0.5000e4 -0.17e2 / 0.2500e4 -0.36894656431e11 / 0.1036385280000e13 0.89277540287e11 / 0.37309870080000e14 0.38859042469e11 / 0.1036385280000e13 0.33048158431e11 / 0.3109155840000e13 -0.4358988450443e13 / 0.65292272640000e14 0.97822819709e11 / 0.487710720000e12 -0.7519148725913e13 / 0.9327467520000e13 0;];
6009f2712d13 Moved and renamned all implementations.
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25
6009f2712d13 Moved and renamned all implementations.
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26 Q(1:11,1:11)=Q_U;
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27 Q(m-10:m,m-10:m)=rot90( -Q_U ,2 );
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29 D1=H\Q;
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32 % s18=-1.000000000000000; s19=0.195000000000000; % alpha 0.0605
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33 s18= -0.475000000000000; s19=0.110000000000000; % alpha 0.0350
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34 %s18=0;s19=0;
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35 DS=sparse(m,m);
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36 DS(1,1:9)=[0.49e2 / 0.20e2 - s18 - (7 * s19) -0.6e1 + 0.7e1 * s18 + (48 * s19) 0.15e2 / 0.2e1 - 0.21e2 * s18 - (140 * s19) -0.20e2 / 0.3e1 + 0.35e2 * s18 + (224 * s19) 0.15e2 / 0.4e1 - 0.35e2 * s18 - (210 * s19) -0.6e1 / 0.5e1 + 0.21e2 * s18 + (112 * s19) 0.1e1 / 0.6e1 - 0.7e1 * s18 - (28 * s19) s18 s19;];
6009f2712d13 Moved and renamned all implementations.
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37 DS(m,m-8:m)=fliplr(DS(1,1:9));
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38 DS=DS/h;
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39
6009f2712d13 Moved and renamned all implementations.
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40 M_U = [0.12056593789671863908e1 -0.13378814169347239658e1 0.36847309286546532061e-2 0.15698288365600946515e0 -0.37472461482539197952e-2 -0.62491712449361657064e-2 -0.29164045872729581661e-1 0.54848184117832929161e-3 0.13613461413384884448e-1 -0.25059220258337808220e-2 -0.94113457993630916498e-3; -0.13378814169347239658e1 0.21749807117105597139e1 -0.12369059547124894597e0 -0.83712574037924152603e0 0.50065127254670973258e-1 0.81045853127317536361e-2 0.97405846039248226536e-1 -0.68942461520402214720e-3 -0.41326971493379188475e-1 0.75778529605774119402e-2 0.25800256160095691057e-2; 0.36847309286546532061e-2 -0.12369059547124894597e0 0.18361596652499065332e0 0.48289690013342693109e-1 -0.19719621435164680412e0 0.11406859029505842791e0 -0.29646295985488126964e-1 -0.16038463172861201306e-2 0.32879841528337653050e-2 -0.93242311589807387463e-3 0.12241332668787820533e-3; 0.15698288365600946515e0 -0.83712574037924152603e0 0.48289690013342693109e-1 0.12886524606662484673e1 -0.14403037739488789185e0 -0.44846291607489015475e0 -0.10598334599408054277e0 -0.15873275740355918053e-1 0.73988493386459608166e-1 -0.12508848749152899785e-1 -0.39290233894513005339e-2; -0.37472461482539197952e-2 0.50065127254670973258e-1 -0.19719621435164680412e0 -0.14403037739488789185e0 0.51482665719685186210e0 0.51199577887125103015e-1 -0.36233561810883077365e0 0.91356850268746392169e-1 0.24195916108052419451e-2 -0.18564214413731389338e-2 -0.70192677320704413827e-3; -0.62491712449361657064e-2 0.81045853127317536361e-2 0.11406859029505842791e0 -0.44846291607489015475e0 0.51199577887125103015e-1 0.68636003380365860083e0 -0.28358848290867614908e0 -0.13836006478253396528e0 0.76158070663111995297e-2 0.11447010307180005164e-1 -0.21349696610286552676e-2; -0.29164045872729581661e-1 0.97405846039248226536e-1 -0.29646295985488126964e-1 -0.10598334599408054277e0 -0.36233561810883077365e0 -0.28358848290867614908e0 0.15216081480839085990e1 -0.42653865162216293237e0 -0.42047484981879143123e0 0.19813359263872926304e-1 0.19221397241190103344e-1; 0.54848184117832929161e-3 -0.68942461520402214720e-3 -0.16038463172861201306e-2 -0.15873275740355918053e-1 0.91356850268746392169e-1 -0.13836006478253396528e0 -0.42653865162216293237e0 0.10656733504627815335e1 -0.66921872668484232217e0 0.12022033144141336599e0 -0.30157881394591483631e-1; 0.13613461413384884448e-1 -0.41326971493379188475e-1 0.32879841528337653050e-2 0.73988493386459608166e-1 0.24195916108052419451e-2 0.76158070663111995297e-2 -0.42047484981879143123e0 -0.66921872668484232217e0 0.24064247712949611684e1 -0.15150200315922263367e1 0.17373015320416595052e0; -0.25059220258337808220e-2 0.75778529605774119402e-2 -0.93242311589807387463e-3 -0.12508848749152899785e-1 -0.18564214413731389338e-2 0.11447010307180005164e-1 0.19813359263872926304e-1 0.12022033144141336599e0 -0.15150200315922263367e1 0.27682502485427255096e1 -0.15975407111468405444e1; -0.94113457993630916498e-3 0.25800256160095691057e-2 0.12241332668787820533e-3 -0.39290233894513005339e-2 -0.70192677320704413827e-3 -0.21349696610286552676e-2 0.19221397241190103344e-1 -0.30157881394591483631e-1 0.17373015320416595052e0 -0.15975407111468405444e1 0.29033627686681129471e1;];
6009f2712d13 Moved and renamned all implementations.
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41
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42
267
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diff changeset
43 % M=-(1/3150)*diag(ones(m-5,1),5)+(5/1008)*diag(ones(m-4,1),4)-(5/126)*diag(ones(m-3,1),3)+(5/21)*diag(ones(m-2,1),2)-(5/3)*diag(ones(m-1,1),1)...
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
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44 % -(1/3150)*diag(ones(m-5,1),-5)+(5/1008)*diag(ones(m-4,1),-4)-(5/126)*diag(ones(m-3,1),-3)+(5/21)*diag(ones(m-2,1),-2)-(5/3)*diag(ones(m-1,1),-1)...
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
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45 % +(5269/1800)*diag(ones(m,1),0);
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46
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
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47 diags = -5:5;
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
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48 left_stencil = [-1/3150,5/1008,-5/126,5/21,-5/3];
f7ac3cd6eeaa Sparsified all implementation files, removed all matlab warnings, fixed small bugs on minimum grid points.
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49 stencil = [left_stencil,5269/1800,fliplr(left_stencil)];
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50 M = stripeMatrix(stencil, diags, m);
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51
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52 M(1:11,1:11)=M_U;
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53 M(m-10:m,m-10:m)=rot90( M_U(1:11,1:11) ,2 );
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54
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55 D2=H\(-M/h+DS);
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56
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57 e_1 = sparse(m,1);
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58 e_1(1)= 1;
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59 e_m = sparse(m,1);
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60 e_m(end)= 1;
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61 S_1 = -DS(1,:)';
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62 S_m = DS(end,:)';
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63
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64 Q = H*D1-(-(e_1*e_1') + (e_m*e_m'));
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65 M = -(H*D2-(-e_1*S_1' + e_m*S_m'));
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66 end