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annotate +time/+sbp/sbpintime.m @ 1198:2924b3a9b921 feature/d2_compatible

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Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents f908ce064f35
children
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365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
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1 % Takes one time step of size k using the sbp in time method
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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2 % starting from v_0 and where
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
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3 % M v_t = E_r'*v + f(t)
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
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4 function v = sbpintime(v, t, tvec, penalty, f, Nblock, E_r,...
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Martin Almquist <martin.almquist@it.uu.se>
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5 L, U, P, Q)
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Martin Almquist <martin.almquist@it.uu.se>
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6
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Martin Almquist <martin.almquist@it.uu.se>
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7 % Pick out last time step
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
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8 v_r = E_r'*v;
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Martin Almquist <martin.almquist@it.uu.se>
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9
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Martin Almquist <martin.almquist@it.uu.se>
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10 % Form RHS
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Martin Almquist <martin.almquist@it.uu.se>
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11 RHS = penalty*v_r;
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Martin Almquist <martin.almquist@it.uu.se>
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12
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Martin Almquist <martin.almquist@it.uu.se>
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13 % Build vector of f-values and add to RHS
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Martin Almquist <martin.almquist@it.uu.se>
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14 if(~isempty(f))
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Martin Almquist <martin.almquist@it.uu.se>
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15 fvec = [];
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Martin Almquist <martin.almquist@it.uu.se>
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16 for i = 1:Nblock
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Martin Almquist <martin.almquist@it.uu.se>
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17 fvec = [fvec;f(t+tvec(i))];
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Martin Almquist <martin.almquist@it.uu.se>
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18 end
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Martin Almquist <martin.almquist@it.uu.se>
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19 RHS = RHS + fvec;
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Martin Almquist <martin.almquist@it.uu.se>
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20 end
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Martin Almquist <martin.almquist@it.uu.se>
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21
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Martin Almquist <martin.almquist@it.uu.se>
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22 % Solve system
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Martin Almquist <martin.almquist@it.uu.se>
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23 %v = M\RHS;
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Martin Almquist <martin.almquist@it.uu.se>
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24 RHS = P*RHS;
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Martin Almquist <martin.almquist@it.uu.se>
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25 RHS = L\RHS;
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Martin Almquist <martin.almquist@it.uu.se>
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26 v = U\RHS;
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Martin Almquist <martin.almquist@it.uu.se>
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27 v = Q*v;
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Martin Almquist <martin.almquist@it.uu.se>
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