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object --+ | DarcyFlow
solves the problem
u_i+k_{ij}*p_{,j} = g_i u_{i,i} = f
where p represents the pressure and u the Darcy flux. k represents the permeability,
Note: The problem is solved in a least squares formulation.
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float
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Data |
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float
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tuple of Data.
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Inherited from |
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Inherited from |
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initializes the Darcy flux problem
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returns the absolute tolerance
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returns the flux for a given pressure
Note: the method uses the least squares solution u=(I+D^*D)^{-1}(D^*f-g-Qp) where D is the div operator and (Qp)_i=k_{ij}p_{,j} for the permeability k_{ij} |
Returns the solver options used to solve the flux problems (I+D^*D)u=F
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Returns the solver options used to solve the pressure problems (Q^*Q)p=Q^*G
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returns the relative tolerance
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sets the absolute tolerance |g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) where
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Sets the solver options used to solve the flux problems (I+D^*D)u=F If
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if the adaption of subtolerance is choosen, the tolerance set by
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Sets the solver options used to solve the pressure problems (Q^*Q)p=Q^*G If
Note:
if the adaption of subtolerance is choosen, the tolerance set by
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sets the relative tolerance |g-v-Qp| <= atol + rtol * min( max( |g-v|, |Qp| ), max( |v|, |g-Qp| ) ) where
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assigns values to model parameters
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solves the problem. The iteration is terminated if the residual norm is less then self.getTolerance().
Note: The problem is solved as a least squares form (I+D^*D)u+Qp=D^*f+g Q^*u+Q^*Qp=Q^*g where D is the div operator and (Qp)_i=k_{ij}p_{,j} for the permeability k_{ij}. We eliminate the flux form the problem by setting u=(I+D^*D)^{-1}(D^*f-g-Qp) with u=u0 on location_of_fixed_flux form the first equation. Inserted into the second equation we get Q^*(I-(I+D^*D)^{-1})Qp= Q^*(g-(I+D^*D)^{-1}(D^*f+g)) with p=p0 on location_of_fixed_pressure which is solved using the PCG method (precondition is Q^*Q). In each iteration step PDEs with operator I+D^*D and with Q^*Q needs to be solved using a sub iteration scheme. |
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