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tutorial9
This tutorial introduces the following concepts:
- Third party **direct** linear equations solvers
Currently there are the following linear equations solvers available:
- SuperLU: sequential sparse direct solver defined in pySuperLU module (BSD licence)
- SuperLU_MT: multi-threaded sparse direct solver defined in pySuperLU_MT module (BSD licence)
- Trilinos Amesos: sequential sparse direct solver defined in pyTrilinos module (GNU Lesser GPL)
- IntelPardiso: multi-threaded sparse direct solver defined in pyIntelPardiso module (proprietary)
- Pardiso: multi-threaded sparse direct solver defined in pyPardiso module (proprietary)
In this example we use the same conduction problem as in the tutorial 1.
The temperature plot (at t=100s, x=0.5, y=*):
.. image:: _static/tutorial9-results.png
:width: 500px
$\mathit{tutorial9}$BC_bottomNeumann boundary conditions at the bottom edge (constant flux)${\mathit{BC}}_{\mathit{bottom}}$eAlgebraic$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { x, y } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_b } } = 0; {\forall { x } \in \left( { x } _{0}, { x } _{n} \right) }, {{ y } = { y } _{0}}$$x$\mathit{x}$$\mathit{x}$
xeOpenOpeny$\mathit{y}$$\mathit{y}$
yeLowerBoundBC_topDirichlet boundary conditions at the top edge (constant temperature)${\mathit{BC}}_{\mathit{top}}$eAlgebraic$${ { T \left( { x, y } \right) } - { T_t } } = 0; {\forall { x } \in \left( { x } _{0}, { x } _{n} \right) }, {{ y } = { y } _{n}}$$x$\mathit{x}$$\mathit{x}$
xeOpenOpeny$\mathit{y}$$\mathit{y}$
yeUpperBoundBC_leftNeumann boundary conditions at the left edge (insulated)${\mathit{BC}}_{\mathit{left}}$eAlgebraic$${ { \partial { { \left( { T \left( { x, y } \right) } \right) } } } \over { \partial {x} } } = 0; {{ x } = { x } _{0}}, {\forall { y } \in \left[ { y } _{0}, { y } _{n} \right] }$$x$\mathit{x}$$\mathit{x}$
xeLowerBoundy$\mathit{y}$$\mathit{y}$
yeClosedClosedBC_rightNeumann boundary conditions at the right edge (insulated)${\mathit{BC}}_{\mathit{right}}$eAlgebraic$${ { \partial { { \left( { T \left( { x, y } \right) } \right) } } } \over { \partial {x} } } = 0; {{ x } = { x } _{n}}, {\forall { y } \in \left[ { y } _{0}, { y } _{n} \right] }$$x$\mathit{x}$$\mathit{x}$
xeUpperBoundy$\mathit{y}$$\mathit{y}$
yeClosedClosed