Functions in emap5.c

Table of Contents

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()

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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()

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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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