Table of Contents

1. ComputeBddMatrix()
2. ComputeCMatrix()
3. ComputeCorrectionTerm()
4. ComputeDMatrix()
5. ComputeGaussQuadPoint()
6. ComputeNonSingul()
7. ComputeNonSingul1()
8. ComputeParameters()
9. ComputeSingul()
10. ComputeSourceVector()
11. ComputeTetraHedronVolume()
12. ComputeTrngleCentroid
13. ConjugateSolver()
14. CreateRHSVector()
15. FEMMatrixCompute()
16. InnerProduct()
17. InvertMatrix()
18. MatrixVectorProduct()
19. PrintOuput()
20. ReadInputFile()
21. SearchNonZeroElement()
22. SurfaceFieldCompute()
23. TetFaceAreaNormal()
24. VectorNorm()

ComputeBddMatrix()

Prototype:   void ComputeBddMatrix(int ObservTrngle, int SourceTrngle,
                                double *ObsTrngleEdgeLen, double *SrcTrngleEdgeLen,
                                int *ObservTrngleNode, int *SourceTrngleNode,
                                int *ObservTrngleEdge, int *SourceTrngleEdge,
                               double *SrcTrngleNorm, double BE[][3] )
Description:    Compute the B matrix generated by FEM. Only Bdd has non-zero
                elements, thus only store Bdd.
Input value:
    int ObservTrngle, SourceTrngle --- the source and observing triangle
                                       indices to the trianle table
    double *ObsTrngleEdgeLen  --- the observing triangle's edge length
    double *SrcTrngleEdgeLen  --- the source triangle's edge length
    int *ObservTrngleNode  --- the observing triangle's nodes
    int *SourceTrngleNode  --- the source triangle's nodes
    int *ObservTrngleEdge  --- the observing triangle's edges
    int *SourceTrngleEdge  --- the source triangle's edges
    double *SrcTrngleNorm   --- the normal vector of the source triangle.
    double BE[][3]  --- to store the results of BE for this triangle pair.
Return value:     none
Global value used:  NodeCord, Junction, Bdd,
                    GlobalEdgeEnds, TrngleCenTroid,
Global value modified:      none
Subroutines called:    sign(),  TrngleArea(), VTXdot()

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ComputeCMatrix()

Prototype:  void ComputeCMatrix(int ObservTrngle, int SourceTrngle,
                    double *ObsTrngleEdgeLen, double *SrcTrngleEdgeLen,
                    int *ObservTrngleNode, int *SourceTrngleNode,
                    int *ObservTrngleEdge, int *SourceTrngleEdge,
                    double **ObsPointArray)
Description:   Fill the Moment Method matrix C, partition it to
               Ccc, Ccd, Cdd and  Cdc.
Input value:
    int ObservTrngle, SourceTrngle --- the source and observing triangle
                                       indices to the trianle table
    double *ObsTrngleEdgeLen  --- the observing triangle's edge length
    double *SrcTrngleEdgeLen  --- the source triangle's edge length
    int *ObservTrngleNode  --- the observing triangle's nodes
    int *SourceTrngleNode  --- the source triangle's nodes
    int *ObservTrngleEdge  --- the observing triangle's edges
    int *SourceTrngleEdge  --- the source triangle's edges
    double **ObsPointArray --- the observing triangle's Gaussian Quadrature
                               point array
Return value:  none
Global value used:     TrngleNode,TrngleNormal,TotQuadPoint,
                       TrngleCenTroid, NodeCord, Ccc, Ccd,  Cdd, Cdc.
Global value modified:     none
Subroutines called:     ComputeGaussQuadPoint(),ComputeSingul(),
                        COMplex_Cmplx(), ComputeNonSingul(), COMplex_Add2(),
                        COMplex_Sub(), COMplex_Null()

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ComputeCorrectionTerm()

Prototype:    void    ComputeCorrectionTerm()
Description:     To couple the MoM matrix equation to the FEM matrix equation. The main idea is to obtain J_d  from C and D. Then couple to the FEM matrix.
Input value:     none
Return value:     none
Global value used:     C_cc, C_cd, C_dc, C_dd, B_dd, TotExtMetalEdgeNum, HybrdBoundEdgeNum, G_d
Global value modified:    InvertMatrix(), COMplex_Add()
Subroutines called:     none.

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ComputeDMatrix()

Prototype: void ComputeDMatrix(int  ObservTrngle, int SourceTrngle,
                    double *ObsTrngleEdgeLen, double *SrcTrngleEdgeLen,
                    int *ObservTrngleNode, int *SourceTrngleNode,
                    int *ObservTrngleEdge, int *SourceTrngleEdge,
                    double **ObsPointArray, double BE[][3])
Description:    Fill D matrix generated by MOM. Partition it to Dcd and Ddd.
Input value:
    int ObservTrngle, SourceTrngle --- the source and observing triangle
                                       indices to the trianle table
    double *ObsTrngleEdgeLen  --- the observing triangle's edge length
    double *SrcTrngleEdgeLen  --- the source triangle's edge length
    int *ObservTrngleNode  --- the observing triangle's nodes
    int *SourceTrngleNode  --- the source triangle's nodes
    int *ObservTrngleEdge  --- the observing triangle's edges
    int *SourceTrngleEdge  --- the source triangle's edges
    double **ObsPointArray --- the observing triangle's Gaussian Quadrature
                               point array
    double BE[][3]  --- store the results of BE for this triangle pair.
Return value:   none
Global value used:   Junction,  NordCord, Ddd, Dcd,
Global value modified:     none
Subroutines called:   sign(),  Real_Mul(), computeNonSingul1(),
                      COMplex_Add2(), COMplex_Null(),
                      ComputeGaussQuadPoint().

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ComputeGaussQuadPoint()

Prototype:    void    ComputeGaussQuadPoint(int QuadPoint, int *TrngleNode, double *SrcPointCol)
Description: To compute the coordinates of 7-point Gauss nodes of a triangular patch.
Input value:

• int QuadPoint  --- node index, it can be from 0 to 6.
• int *TrngleNode  ---  the three nodes of a tringular patch.
• double *SrcPointCol --- where to store the results

Return value: none
Global value used: NodeCord, Qpnt
Global value modified:    none
Subroutines called:    none
Note: Not very sure.
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ComputeNonSingul()

Prototype:    void    ComputeNonSingul(int *TrngleNode, double One, double *MidPoint)
Description: To evaluate the MOM surface integral numerically when the observation triangle and the source triangle are different.
Input value:

• int *TrngleNode --- nodes of the source triangle
• double One  --- a factor
• double *MidPoint --- middle point of the observing trianlge

Return value: none
Global value used: none
Global value modified: none
Subroutines called: COMplex_add(), COMplex_Cmplx(), COMplex_Expon(), Real_Mul(), COMplex_Sub()

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ComputeNonSingul1()

Prototype: void ComputeNonSingul(int *TrngleNode, double One,
                                 double *MidPoint, complex *Ino_PQ,
                                 complex *Ixi_PQ,
                                 complex *Ieta_PQ, complex *Izeta_PQ)
Description: To evaluate the MOM surface integral numerically when the
             observation triangle and the source triangle are different.
Input value:
    int *TrngleNode --- nodes of the source triangle
    double One  --- a factor
    double *MidPoint --- middle point of the observing trianlge
Return value:
    complex *Ino_PQ   --- to store the value of Ino
    complex *Ixi_PQ   --- to store the value of Ixi
    complex *Ieta_PQ  --- to store the value of Ieta
    complex *Izeta_PQ --- to store the value of Izeta.
    The above values are used in ComputeCMatrix().
Global value used: none
Global value modified: none
Subroutines called: COMplex_add(), COMplex_Cmplx(), COMplex_Expon(),
                    Real_Mul(), COMplex_Sub()
 

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ComputeParameters()

Prototype:    void    ComputeParameters()
Description:    To computes parameters(TetVolume, TrngleArea, TrngleCentroid and etc) which are necessary to build the FEM matrix and MOM matrix,
Input value:    none
Return value:    none
Global value used:     AbsPermeable, AbsPermitt, CFactor1, CFactor2, Cfactor3, EdgeLength, FreeSpaceVel, ImpeDance, NodeCord, OperateFreq, GlobalEdgeEnds, TetLocalEdge, TetLocalNodeNum, TetVolume, TotEdgeNum, TotTetElement, TotTrnlgeNum,TParam, TrngleArea, TrngleCentroid, WaveLength, WaveNumber,
Global value modified:     CFactor1, CFactor2, Cfactor3, FreeSpaceVel, TetVolume, TrngleArea, TrngleCentroid,
Subroutines called:     COMplex_Cmplx(), ComputeTetraHeronVolume(), ComputeTrngleCentroid(), Real_Mul() TetfaceAreaNormal(), VTXmag()

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ComputeSingul()

Prototype:    void    ComputeSingul(int *Node, double *MidPoint, double AREA)
Description:     To evaluate the singularity of the MOM integral analytically when the observing triangle coincides with the source triangle. The results are stored in global variables RealIno, RealIxi and RealIeta.
Input value:

• int *Node --- the nodes of the triangle
• double *MidPoint --- middle point of the triangle
• double AREA --- the area of the triangle

Return value: none
Global value used: double **NodeCord
Global value modified: RealIno, RealIxi, RealIeta
Subroutines called: none

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ComputeSourceVector()

Prototype:    void    ComputeSourceVector(double WaveNum, double *MidPoint, complex *EiC)
Description:     To compute the E fields of an incident plane wave at the boundary surface.
Input value:

• double WaveNum --- wavenumber of the plane wave.
• double MidPoint --- midpoint of the observing triangle.
• complex *EiC  --- where to store the results

Return value: none
Global value used: none
Global value modified: none
Subroutines called:  none

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ComputeTetraHedronVolume()

Prototype:    void    ComputeTetraHedronVolume(int TetHedNum, double **Cord, int **TGNodeNum,double *TVolume)
Description:    To calculate the volume of a tetrahedron
Input value:

• int TetHedNum --- the number of  the tetrahedron
• double **cord  --- the global node table
• int **TGNodeNum --- the global node numbers of the tetrahedron
• double *TVolume, -- where to store the results.

Return value:     none
Global value used:     none
Global value modified:     none
Subroutines called:     VTXsub1()

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ComputeTrngleCentroid()

Prototype:    void    ComputeTrngleCentroid( int TrngleNum, double **Cord, int **BFaceNode, double **CenTroid)
Description:     To compute the centroid of a triangular patch.
Input value:

• int TrngleNum   --- the number of the triangle
• double **Cord  --- the gloabl node table
• int BFaceNode  --- the nodes of the triangle
• double **Centroid -- where to store the results

Return value:    none
Global value used:    none
Global value modified:    none
Subroutines called:     VTXadd2()

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ConjugateSolver()

Prototype:    void    ConjugateSolver(int MatrixSize, int *RowIIndex, int **RowICol, complex **RowIDat, complex *RHSVec, int ITmax, double TOL)
Description:     To solve a linear system using complex bi-conjugate gradient method.
Input value:

• int MatrixSize--- the size of the matrix equation.
• complex **RowIDat, int **RowICol, int *RowIIndex --- the FEM matrix stored using the row-indexed scheme
• complex *RHSVec----  the right-hand side vector, the results are stored in this vector.
• int ITmax  --- the maximum iteration number. If the solver runs the maximum iterations but still has not reach the tolerance, the solver will return and store the best results.
• double TOL  --- the tolerance. If the solver reaches in the tolerance, it will stop and store the results.

Return value:     none
Global value used:     none
Global value modified:     none
Subroutines called:     CMPLX_Vector(), COMplex_Cmplx(), COMplex_Null(), COMplex_Sub(), COMplex_Conjg(), VectorNorm(), InnerProduct(), COMplex_Add(), COMplex_Div(), COMplex_Mul(),
Real_Div().

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CreateRHSVector()

Prototype:    void    CreateRHSVector(int InnerEdgeNum, int BoundEdgeNum, int ForcdEdgeNum, complex **FCDMatrixData, complex **ForcdValue,complex *RHSVector)
Description:     To use boundary conditions to create the right-hand side vector. The final matrix equation is  [LHS][E]=[RHS]. After RHS is known,  [E] can be solved by using  ConjugateSolver() .
Input value:

• int InnerEdgeNum, -- number of total inner edges
• int BoundEdgeNum, ---number of total surface edges
• int ForcdEdgeNum---number of total forced edges

Return value: none
Global value used:     SourceType ,GdVector, TotInnerEdgeNum
Global value modified:     none
Subroutines called:     COMplex_Mul(), COMplex_Add(), COMplex_Null(), Real_Mul() (Click to go back to Table of Contents.)

FEMMatrixCompute()

Prototype:    void    FemMatrixCompute(int NumOfTetElement, int MaxElementPerRow, int **TetEdge, int **GlobalEdgeEnds,double **NodeCord, complex *TParam, complex *Epsilon, int **GBLmatColAddr, complex **GBLmat, int *GBLmatColIndex, double *TetVolume)
Description:     To build the FEM matrix and store them using row-indexed scheme.
Input value:

• int NumOfTetElement --- total number of tetrahedron elements
• int MaxElementPerRow --- the FEM matrix is a sparse matrix. Every row has a maximum number (MaxElementPerRow) of non-zero elemnet. Only non-zero elements are stored
• int **TetEdge --- the edge table of tetrahedron elements
• int **GlobalEdgeEnds --- global edge table
• double **NodeCord, --- global node table
• complex *TParam, --- store constants used by FEM
• complex *Epsilon, --- the permittivity associated with each tetrahedron element.
• int **GBLmatColAddr, complex **GBLmat, int *GBLmatColIndex,--- the FEM matrix stored using row-indexed  scheme.
• double *TetVolume ---the volume of tetrahedron elements

Return value:     void
Global value used:     none
Global value modified: none
Subroutines called:     VTXsub(), VTXcross(), Sign()

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MatrixVectorProduct()

Prototype:  void MatrixVectorProduct(char S, int Size, complex *XVec, complex *AVec, int *RIIndex,int **RICol,complex **RIDat)
Description:    To multiply the final matrix equation { [FEM] +[C_dd] } with a vector.
Input value:

• complex **RIDat, int RIIndex, int **RICol --- the FEM matrix stored using the row-indexed scheme.
• complex *XVec --- pointer to a vector of complex type
• complex *AVec --- where the results are stored.
• int Size  --- the dimension of the vectors.  The vector and the matrix should have the same dimension.
• char S --- operation type. If s== '  ',  return [A]={[FEM] +[C_dd] }[X]. If S='*', return [A]={[FEM] +[C_dd] }*[X], where * denoteds conjugate.

Return value:   none
Global value used:  C_dd
Global value modified:     none
Subroutines called:   COMplex_Add(), COMplex_Null(), COMplex_Mul(), COMplex_Conjg()

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InnerProduct()

Prototype:     complex Inner_Prod( complex *AVec,  complex *BVec, int Size )
Description:    To compute the inner product of  two vectors of complex type.
Input value:

• complex *AVector, *BVector --- two vectors of complex type, they should have the same length
• int Size  --- the length of the vectors.

Return value:   return the inner product of the two vectors.
                         If B=(x1, x2, ... xn), A=(y1, y2, ..., yn),
                         The inner product is defined as   x1y1* + x2y2* + ... +xnyn*, where * denotes conjugate.
Global value used:  none
Global value modified:     none
Subroutines called:   COMplex_Add().

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InvertMatrix()

Prototype:    void    InvertMatrix(complex **Qmat, int MatrixSize)
Description:    To invert a complex matrix. The results are stored in the input matrix, thus no additional memory needed.
Input value:

• complex **Qmat --- a complex matrix
• int matrixSize --- the size of the matrix

Return value:     none
Global value used:     none
Global value modified:     none
Subroutines called:    COMplex_Abs(), COMplex_Div(), COMplex_Cmplx(), COMplex_Sub(), COMplex_Mul(), INT_Matrix(), free_INT_Matrix() (Click to go back to Table of Contents.)

PartitionGlobalFEMMatrix()

Prototype:     void    PartitionGlobalFEMMatrix(int ** GBLmatColAddr, complex **GBLmat, int *GBLmatColIndex, int InnerEdgeNum, int BoundEdgeNum, int ForcdEdgeNum, int *InnerEdgeStat, int *BoundEdgeStat, int *ISourceEdgeStat, complex **LHSMatrixData, complex **FCDMatrixData, complex **Cdd )
Description:     Partition the FEM matrix in terms of the internal, boundary and far-field quantities
Input value:

• int ** GBLmatColAddr, complex **GBLmat, int *GBLmatColIndex -- the FEM matrix stored using the row-indexed scheme.
• int InnerEdgeNum --- number of total inner edges
• int BoundEdgeNum --- number of total boundary edges
• int ForcdEdgeNum --- number of total forced edges
• int *InnerEdgeStat --- the global edge indices of the inner edges
• int *BoundEdgeStat --- the global edge indices of the boundary edges
• int *ISourceEdgeStat --- the global edge indices of the forced edges
• complex **LHSMatrixData --- put the results into this matrix
• complex **FCDMatrixData --- forced edge values
• complex **Cdd --- submatrix of C

Return value:     none
Global value used:     GBLmatColAddr, GBLmat, GBLmatColIndex, TotInnerEdgeNUm, DielBoundEdgeNum, TotISourceEdgeNum, InnerEdgeStat, BoundEdgeStat, ISourceEdgeStat, LHSMatrixData, FCDMAtrixData, Cdd
Global value modified:     none
Subroutines called:     Search NonZeroElement(), COMplex_Add()

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ReadInputFile()

Prototype:    void    ReadMeshFile()
Description:    To read data from an input  file, initialize global variables
Input value:     none
Return value:     none
Global value used:     TotEdgeNum, TotTetElement, TotNodeNum, TotTrngleNum, TotBoundEdgeNum, TotInnerEdgeNum, DielBoundEdgeNum, HybrdBoundEdgeNum, TrngleNode,TrngleEdge,NodeCord, TetNode, TetNode,Epsilon, TetEdge , GlobalEdgeEnds, PlusTrngleDet, PlusTrngleIndex,MinusTrngleDet, MinusTrngleIndex,InnerEdgeStat,BoundEdgeStat,SourceType,VsourceMag, VSourceNum, OperateFreq, VsourceEdge,VVal
Global value modified:     TotEdgeNum, TotTetElement, TotNodeNum, TotTrngleNum, TotBoundEdgeNum, TotInnerEdgeNum, DielBoundEdgeNum, HybrdBoundEdgeNum, TrngleNode,TrngleEdge,NodeCord, TetNode, TetNode,Epsilon, TetEdge , GlobalEdgeEnds, PlusTrngleDet, PlusTrngleIndex,MinusTrngleDet, MinusTrngleIndex,InnerEdgeStat,BoundEdgeStat,SourceType,VsourceMag, VSourceNum, OperateFreq, VsourceEdge,VVal
Subroutines called:     INT_Matrix(), INT_Vector()

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PrintOutput()

Prototype:     void   PrintOutput()
Description:   To print out the field within the area specified by the input file .
Input value:     none
Return value:   none
Global value used:  InF, OutF, HybrdBoundEdgeNum, EdVector, JdVector, JcVector, GlobalEdgeEnds, HybrdBoundEdgeNum, TotInnerEdgeNum, NodeCord, RHSVector
Global value modified:     none
Subroutines called:  none

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SearchNonZeroElement()

Prototype:    int    SearchNonZeroElement(int RowNum, int ColNum)
Description:     To search an element in the global FEM matrix. To conserve memory, only none-zero elements are stored in the FEM matrix using row-indexed scheme.  If the element is found, return the column index to the global FEM matrix. Otherwise, return -1.
Input value:

• int RowNum --- row number, which is assigned to the observing edge
• int ColNum ---  column number, which is assigned to the source edge.

Return value:  the column index to GBLmat.
Global value used: int *GBLmatColIndex, int *GBLmatColAddr
Global value modified: none
Subroutines called: none

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SurfaceFieldCompute()

Prototype:  void  SurfaceFieldCompute()
Description:  To compute the equivalent surface current density (Jc and Jd )
Input value:  none
Return value:  none
Global value used:  TotInnerEdgeNum EdVector HybrdBoundEdgeNum,
                    JdVector, JcVector,TotExtMetalEdgeNum, Dcd,  EdVector,
Global value modified:  none
Subroutines called:   COMplex_Add(),COMplex_Mul()
 

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TetFaceAreaNormal()

Prototype:    void    TetFaceAreaNormal(int TrngleNum, double **Cord, int **BFaceNode, double **Normal, double *Area)
Description:     To compute the unit normal and the area of each face of the tetrahedron
Input value:

• int TrngleNum --- index of the tetrahedron
• double **Cord --- the global node table
• int **BFaceNode  --- the nodes of each face
• double **Normal -- where to store the centroid of each face
• double *Area  --- where to store the area of each face

Return value:    none
Global value used:     none
Global value modified:     none
Subroutines called:     VTXcross1(), VTXsub1(), VTXcross()

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VectorNorm()

Prototype:    double VectorNorm(complex *Vec, int Size)
Description:     To compute the the Euclidean norm of a complex vector
Input value:

• complex *Vec  --- pointer to a vector of complex type
• int Size  ---  the length of the vector

Return value:    the Euclidean norm of the vector. If the vector is (x1, x2, ..., xn),
                          the norm is defined as sqrt( |x1|^2 +|x2|^2+...+|xn|^2).
Global value used:     none
Global value modified:     none
Subroutines called:     COMplex_Abs().

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