\( D_{0} \) matricial representation More...
#include <dzero.hpp>
Inheritance diagram for DZero:
Collaboration diagram for DZero:
Public Member Functions | |
| DZero (Size gridPoints, Real h) | |
| Public Member Functions inherited from TridiagonalOperator | |
| TridiagonalOperator (Size size=0) | |
| TridiagonalOperator (const Array &low, const Array &mid, const Array &high) | |
| TridiagonalOperator (const TridiagonalOperator &)=default | |
| TridiagonalOperator (TridiagonalOperator &&) noexcept | |
| TridiagonalOperator & | operator= (const TridiagonalOperator &) |
| TridiagonalOperator & | operator= (TridiagonalOperator &&) noexcept |
| ~TridiagonalOperator ()=default | |
| Size | size () const |
| bool | isTimeDependent () const |
| const Array & | lowerDiagonal () const |
| const Array & | diagonal () const |
| const Array & | upperDiagonal () const |
| void | setFirstRow (Real, Real) |
| void | setMidRow (Size, Real, Real, Real) |
| void | setMidRows (Real, Real, Real) |
| void | setLastRow (Real, Real) |
| void | setTime (Time t) |
| void | swap (TridiagonalOperator &) noexcept |
| Array | applyTo (const Array &v) const |
| apply operator to a given array More... | |
| Array | solveFor (const Array &rhs) const |
| solve linear system for a given right-hand side More... | |
| void | solveFor (const Array &rhs, Array &result) const |
| Array | SOR (const Array &rhs, Real tol) const |
| solve linear system with SOR approach More... | |
Additional Inherited Members | |
| Public Types inherited from TridiagonalOperator | |
| typedef Array | array_type |
| Static Public Member Functions inherited from TridiagonalOperator | |
| static TridiagonalOperator | identity (Size size) |
| identity instance More... | |
| Protected Attributes inherited from TridiagonalOperator | |
| Size | n_ |
| Array | diagonal_ |
| Array | lowerDiagonal_ |
| Array | upperDiagonal_ |
| Array | temp_ |
| ext::shared_ptr< TimeSetter > | timeSetter_ |
Detailed Description
\( D_{0} \) matricial representation
The differential operator \( D_{0} \) discretizes the first derivative with the second-order formula
\[ \frac{\partial u_{i}}{\partial x} \approx \frac{u_{i+1}-u_{i-1}}{2h} = D_{0} u_{i} \]
- Tests:
- the correctness of the returned values is tested by checking them against numerical calculations.
