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tutorial12
This tutorial describes the use and available options for superLU direct linear solvers:
- Sequential: superLU
- Multithreaded (OpenMP/posix threads): superLU_MT
The model is the same as the model in tutorial 1, except for the different boundary conditions.
The temperature plot (at t=100s, x=0.5, y=*):
.. image:: _static/tutorial12-results.png
:width: 500px
$\mathit{tutorial12}$
BC_bottom
Neumann 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
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x
eOpenOpen
y
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y
eLowerBound
BC_top
Neumann boundary conditions at the top edge (constant flux)
${\mathit{BC}}_{\mathit{top}}$
eAlgebraic
$${ \left( { \left( { \left( - { \lambda_p } \right) } \right) \cdot \left( { { \partial { { \left( { T \left( { x, y } \right) } \right) } } } \over { \partial {y} } } \right) } \right) - { Q_t } } = 0; {\forall { x } \in \left( { x } _{0}, { x } _{n} \right) }, {{ y } = { y } _{n}}$$
x
$\mathit{x}$
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eOpenOpen
y
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eUpperBound
BC_left
Neumann 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
$\mathit{x}$
$\mathit{x}$
x
eLowerBound
y
$\mathit{y}$
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eClosedClosed
BC_right
Neumann 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
$\mathit{x}$
$\mathit{x}$
x
eUpperBound
y
$\mathit{y}$
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y
eClosedClosed