Structure

Diffusion matrix 1

$$M(I,J)=\int_{\Omega}\frac{\partial N^{I}}{\partial x_{i}}\frac{\partial N^{J}}{\partial x_{i}}d\Omega$$

Interface:

PURE FUNCTION DiffusionMatrix(test, trial, opt) RESULT(ans)
    CLASS(ElemshapeData_), INTENT(IN) :: test
    CLASS(ElemshapeData_), INTENT(IN) :: trial
    INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
    REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 2

$$M(I,J)=\int_{\Omega}\rho\frac{\partial N^{I}}{\partial x_{i}}\frac{\partial N^{J}}{\partial x_{i}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, k, krank, opt) &
  & RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: k
  !! scalar
  TYPE(FEVariableScalar_), INTENT( IN ) :: krank
  !! scalar fe variable
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 3

$$M(I,J)=\int_{\Omega}\frac{\partial N^{I}}{\partial x_{i}}a_{i}a_{j}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, k, krank, opt) &
  & RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: k
  !! vector
  TYPE(FEVariableVector_), INTENT( IN ) :: krank
  !! vector
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 4

$$M(I,J)=\int_{\Omega}\frac{\partial N^{I}}{\partial x_{i}}k_{ij}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, k, krank, opt) &
  & RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: k
  !! matrix
  TYPE(FEVariableMatrix_), INTENT(IN) :: krank
  !! matrix
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 5

$$M(I,J)=\int\rho_{1}\rho_{2}\frac{\partial N^{I}}{\partial x_{i}}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Scalar
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Scalar
  TYPE(FEVariableScalar_), INTENT( IN ) :: c1rank
  !! Scalar
  TYPE(FEVariableScalar_), INTENT( IN ) :: c2rank
  !! Scalar
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 6

$$M(I,J)=\int\rho\frac{\partial N^{I}}{\partial x_{i}}v_{i}v_{j}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Scalar
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Vector
  TYPE(FEVariableScalar_), INTENT( IN ) :: c1rank
  !! Scalar
  TYPE(FEVariableVector_), INTENT( IN ) :: c2rank
  !! Vector
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 7

$$M(I,J)=\int\rho_{1}\frac{\partial N^{I}}{\partial x_{i}}k_{ij}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Scalar
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Matrix
  TYPE(FEVariableScalar_), INTENT( IN ) :: c1rank
  !! Scalar
  TYPE(FEVariableMatrix_), INTENT( IN ) :: c2rank
  !! Matrix
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 8:

$$M(I,J)=\int\rho\frac{\partial N^{I}}{\partial x_{i}}v_{i}v_{j}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Vector
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Scalar
  TYPE(FEVariableVector_), INTENT( IN ) :: c1rank
  !! Vector
  TYPE(FEVariableScalar_), INTENT( IN ) :: c2rank
  !! Scalar
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 9:

$$M(I,J)=\int\frac{\partial N^{I}}{\partial x_{i}}v_{i}w_{j}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Vector
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Vector
  TYPE(FEVariableVector_), INTENT( IN ) :: c1rank
  !! Vector
  TYPE(FEVariableVector_), INTENT( IN ) :: c2rank
  !! Vector
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 10:

$$M(I,J)=\int\frac{\partial N^{I}}{\partial x_{i}}v_{p}b_{pi}v_{q}b_{qj}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Vector
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Matrix
  TYPE(FEVariableVector_), INTENT( IN ) :: c1rank
  !! Vector
  TYPE(FEVariableMatrix_), INTENT( IN ) :: c2rank
  !! Matrix
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 11:

$$M(I,J)=\int\rho_{1}\frac{\partial N^{I}}{\partial x_{i}}k_{ij}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Matrix
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Scalar
  TYPE(FEVariableMatrix_), INTENT( IN ) :: c1rank
  !! Matrix
  TYPE(FEVariableScalar_), INTENT( IN ) :: c2rank
  !! Scalar
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 12:

$$M(I,J)=\int\frac{\partial N^{I}}{\partial x_{i}}b_{ip}v_{p}b_{jq}v_{q}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

Interface:

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Matrix
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Vector
  TYPE(FEVariableMatrix_), INTENT( IN ) :: c1rank
  !! Matrix
  TYPE(FEVariableVector_), INTENT( IN ) :: c2rank
  !! Vector
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 13:

$$M(I,J)=\int\frac{\partial N^{I}}{\partial x_{i}}b_{ip}c_{pj}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

MODULE PURE FUNCTION DiffusionMatrix(test, trial, c1, c2, c1rank, &
  & c2rank, opt ) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: c1
  !! Matrix
  CLASS(FEVariable_), INTENT(IN) :: c2
  !! Matrix
  TYPE(FEVariableMatrix_), INTENT( IN ) :: c1rank
  !! Matrix
  TYPE(FEVariableMatrix_), INTENT( IN ) :: c2rank
  !! Matrix
  INTEGER( I4B ), OPTIONAL, INTENT( IN ) :: opt
  !! ncopy
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 14:

opt=[1]

$$\left[M\right]_{IJ}^{ij}=\int\frac{\partial N^{I}}{\partial x_{i}}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

opt=[2]

$$\left[M\right]_{IJ}^{ij}=\int\frac{\partial N^{I}}{\partial x_{j}}\frac{\partial N^{J}}{\partial x_{i}}d\Omega$$

MODULE PURE FUNCTION DiffusionMatrix(test, trial, opt) RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  INTEGER( I4B ), INTENT( IN ) :: opt( 1 )
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix

Diffusion matrix 15:

opt=[1]

$$\left[M\right]_{IJ}^{ij}=\int\rho\frac{\partial N^{I}}{\partial x_{i}}\frac{\partial N^{J}}{\partial x_{j}}d\Omega$$

opt=[2]

$$\left[M\right]_{IJ}^{ij}=\int\rho\frac{\partial N^{I}}{\partial x_{j}}\frac{\partial N^{J}}{\partial x_{i}}d\Omega$$

MODULE PURE FUNCTION DiffusionMatrix(test, trial, k, krank, opt) &
  & RESULT(ans)
  CLASS(ElemshapeData_), INTENT(IN) :: test
  !! test function
  CLASS(ElemshapeData_), INTENT(IN) :: trial
  !! trial function
  CLASS(FEVariable_), INTENT(IN) :: k
  !! scalar
  TYPE(FEVariableScalar_), INTENT( IN ) :: krank
  !! scalar fe variable
  INTEGER( I4B ), INTENT( IN ) :: opt(1)
  REAL(DFP), ALLOCATABLE :: ans(:, :)
END FUNCTION DiffusionMatrix