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annotate +rv/+time/rungekuttaRV.m @ 1142:cff49fba3cc8 rv-interpolation

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Closing branch
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 05 Aug 2019 10:49:21 +0200
parents 2d7c1333bd6c
children 010bb2677230
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846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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1 % Takes one time step of size dt using the rungekutta method
1012
1e437c9e5132 Create residual viscosity package +rv and generalize the ResidualViscosity class
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 847
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2 % starting from v and where the function F(v,t,RV) gives the
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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3 % time derivatives. coeffs is a struct holding the RK coefficients
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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4 % for the specific method. RV is the residual viscosity which is updated
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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5 % in between the stages and after the updated solution is computed.
1017
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
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6 function v = rungekuttaRV(v, t , dt, F, RV, DvDt, coeffs)
846
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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7 % Move one stage outside to avoid branching for updating the
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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8 % residual inside the loop.
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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9 k = zeros(length(v), coeffs.s);
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2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
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10 k(:,1) = F(v,t,RV.evaluate(v,DvDt(v)));
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c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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11
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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12 % Compute the intermediate stages k
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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13 for i = 2:coeffs.s
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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14 u = v;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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15 for j = 1:i-1
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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16 u = u + dt*coeffs.a(i,j)*k(:,j);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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17 end
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2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
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18 %RV.update(0.5*(u+v),(u-v)/(coeffs.c(i)*dt)); % Crank-Nicholson for time discretization
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
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19 k(:,i) = F(u,t+coeffs.c(i)*dt, RV.evaluate(u,DvDt(u)));
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c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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20 end
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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21
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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22 % Compute the updated solution as a linear combination
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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23 % of the intermediate stages.
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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24 u = v;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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25 for i = 1:coeffs.s
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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26 u = u + dt*coeffs.b(i)*k(:,i);
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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27 end
1017
2d7c1333bd6c Add support for using the ODE to approximate the time derivative in the residual
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1012
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28 %RV.update(0.5*(u+v),(u-v)/dt); % Crank-Nicholson for time discretization
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c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
29 v = u;
c6fcee3fcf1b Add generalized RungeKutta and RungeKuttaRV class which extracts its coefficients from a butcher tableau, specified on the scheme.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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30 end