base_functions.c File Reference

#include <cblas.h>
#include <petscsys.h>
#include <phg-quadrule/quad.h>
#include <definitions.h>
#include <base_functions.h>

Go to the source code of this file.

Functions
PetscErrorCode	Legendre_polynomials (int p, double s, double *diff_s, double *L, double *diffL, const int dim)
	Calculate Legendre approximation basis. More...
PetscErrorCode	Jacobi_polynomials (int p, double alpha, double x, double t, double *diff_x, double *diff_t, double *L, double *diffL, const int dim)
	Calculate Jacobi approximation basis. More...
PetscErrorCode	IntegratedJacobi_polynomials (int p, double alpha, double x, double t, double *diff_x, double *diff_t, double *L, double *diffL, const int dim)
	Calculate integrated Jacobi approximation basis. More...
PetscErrorCode	Lobatto_polynomials (int p, double s, double *diff_s, double *L, double *diffL, const int dim)
	Calculate Lobatto base functions [29]. More...
static double	f_phi0 (double x)
static double	f_phi1 (double x)
static double	f_phi2 (double x)
static double	f_phi3 (double x)
static double	f_phi4 (double x)
static double	f_phi5 (double x)
static double	f_phi6 (double x)
static double	f_phi7 (double x)
static double	f_phi8 (double x)
static double	f_phi9 (double x)
static double	f_phi0x (double x)
static double	f_phi1x (double x)
static double	f_phi2x (double x)
static double	f_phi3x (double x)
static double	f_phi4x (double x)
static double	f_phi5x (double x)
static double	f_phi6x (double x)
static double	f_phi7x (double x)
static double	f_phi8x (double x)
static double	f_phi9x (double x)
PetscErrorCode	LobattoKernel_polynomials (int p, double s, double *diff_s, double *L, double *diffL, const int dim)
	Calculate Kernel Lobatto base functions. More...

Variables
static PetscErrorCode	ierr
static double(*	f_phi [])(double x)
static double(*	f_phix [])(double x)

Function Documentation

f_phi0()

static double f_phi0 ( double  x )

static

Definition at line 250 of file base_functions.c.

{ return LOBATTO_PHI0(x); }

f_phi0x()

static double f_phi0x ( double  x )

static

Definition at line 264 of file base_functions.c.

{ return LOBATTO_PHI0X(x); }

f_phi1()

static double f_phi1 ( double  x )

static

Definition at line 251 of file base_functions.c.

{ return LOBATTO_PHI1(x); }

f_phi1x()

static double f_phi1x ( double  x )

static

Definition at line 265 of file base_functions.c.

{ return LOBATTO_PHI1X(x); }

f_phi2()

static double f_phi2 ( double  x )

static

Definition at line 252 of file base_functions.c.

{ return LOBATTO_PHI2(x); }

f_phi2x()

static double f_phi2x ( double  x )

static

Definition at line 266 of file base_functions.c.

{ return LOBATTO_PHI2X(x); }

f_phi3()

static double f_phi3 ( double  x )

static

Definition at line 253 of file base_functions.c.

{ return LOBATTO_PHI3(x); }

f_phi3x()

static double f_phi3x ( double  x )

static

Definition at line 267 of file base_functions.c.

{ return LOBATTO_PHI3X(x); }

f_phi4()

static double f_phi4 ( double  x )

static

Definition at line 254 of file base_functions.c.

{ return LOBATTO_PHI4(x); }

f_phi4x()

static double f_phi4x ( double  x )

static

Definition at line 268 of file base_functions.c.

{ return LOBATTO_PHI4X(x); }

f_phi5()

static double f_phi5 ( double  x )

static

Definition at line 255 of file base_functions.c.

{ return LOBATTO_PHI5(x); }

f_phi5x()

static double f_phi5x ( double  x )

static

Definition at line 269 of file base_functions.c.

{ return LOBATTO_PHI5X(x); }

f_phi6()

static double f_phi6 ( double  x )

static

Definition at line 256 of file base_functions.c.

{ return LOBATTO_PHI6(x); }

f_phi6x()

static double f_phi6x ( double  x )

static

Definition at line 270 of file base_functions.c.

{ return LOBATTO_PHI6X(x); }

f_phi7()

static double f_phi7 ( double  x )

static

Definition at line 257 of file base_functions.c.

{ return LOBATTO_PHI7(x); }

f_phi7x()

static double f_phi7x ( double  x )

static

Definition at line 271 of file base_functions.c.

{ return LOBATTO_PHI7X(x); }

f_phi8()

static double f_phi8 ( double  x )

static

Definition at line 258 of file base_functions.c.

{ return LOBATTO_PHI8(x); }

f_phi8x()

static double f_phi8x ( double  x )

static

Definition at line 272 of file base_functions.c.

{ return LOBATTO_PHI8X(x); }

f_phi9()

static double f_phi9 ( double  x )

static

Definition at line 259 of file base_functions.c.

{ return LOBATTO_PHI9(x); }

f_phi9x()

static double f_phi9x ( double  x )

static

Definition at line 273 of file base_functions.c.

{ return LOBATTO_PHI9X(x); }

IntegratedJacobi_polynomials()

PetscErrorCode IntegratedJacobi_polynomials	(	int	p,
		double	alpha,
		double	x,
		double	t,
		double *	diff_x,
		double *	diff_t,
		double *	L,
		double *	diffL,
		const int	dim
	)

Calculate integrated Jacobi approximation basis.

For more details see [30]

Parameters

p	is approximation order
alpha	polynomial parameter
x	is position \(s\in[0,t]\)
t	range of polynomial
diff_x	derivatives of shape functions, i.e. \(\frac{\partial x}{\partial \xi_i}\)
diff_t	derivatives of shape functions, i.e. \(\frac{\partial t}{\partial \xi_i}\)

Return values

L	approximation functions
diffL	derivatives, i.e. \(\frac{\partial L}{\partial \xi_i}\)

Parameters

dim

dimension

Returns

error code

Definition at line 151 of file base_functions.c.

                                                                          {
  MoFEMFunctionBeginHot;
#ifndef NDEBUG
  if (dim < 1)
    SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim < 1");
  if (dim > 3)
    SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim > 3");
  if (p < 1)
    SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "p < 1");
#endif // NDEBUG
  L[0] = x;
  if (diffL != NULL) {
    int d = 0;
    for (; d != dim; ++d) {
      diffL[d * p + 0] = diff_x[d];
    }
  }
  if (p == 0)
    MoFEMFunctionReturnHot(0);
  double jacobi[(p + 1)];
  double diff_jacobi[(p + 1) * dim];
  ierr = Jacobi_polynomials(p, alpha, x, t, diff_x, diff_t, jacobi, diff_jacobi,
                            dim);
  CHKERRQ(ierr);
  int l = 1;
  for (; l < p; l++) {
    int i = l + 1;
    const double a = (i + alpha) / ((2 * i + alpha - 1) * (2 * i + alpha));
    const double b = alpha / ((2 * i + alpha - 2) * (2 * i + alpha));
    const double c = (i - 1) / ((2 * i + alpha - 2) * (2 * i + alpha - 1));
    L[l] = a * jacobi[i] + b * t * jacobi[i - 1] - c * t * t * jacobi[i - 2];
    if (diffL != NULL) {
      int dd = 0;
      for (; dd != dim; ++dd) {
        diffL[dd * p + l] = a * diff_jacobi[dd * (p + 1) + i] +
                            b * (t * diff_jacobi[dd * (p + 1) + i - 1] +
                                 diff_t[dd] * jacobi[i - 1]) -
                            c * (t * t * diff_jacobi[dd * (p + 1) + i - 2] +
                                 2 * t * diff_t[dd] * jacobi[i - 2]);
      }
    }
  }
  MoFEMFunctionReturnHot(0);
}

Jacobi_polynomials()

PetscErrorCode Jacobi_polynomials	(	int	p,
		double	alpha,
		double	x,
		double	t,
		double *	diff_x,
		double *	diff_t,
		double *	L,
		double *	diffL,
		const int	dim
	)

Calculate Jacobi approximation basis.

For more details see [30]

Parameters

p	is approximation order
alpha	polynomial parameter
x	is position \(s\in[0,t]\)
t	range of polynomial
diff_x	derivatives of shape functions, i.e. \(\frac{\partial x}{\partial \xi_i}\)
diff_t	derivatives of shape functions, i.e. \(\frac{\partial t}{\partial \xi_i}\)

Return values

L	approximation functions
diffL	derivatives, i.e. \(\frac{\partial L}{\partial \xi_i}\)

Parameters

dim

dimension

Returns

error code

Definition at line 67 of file base_functions.c.

                                                                {
  MoFEMFunctionBeginHot;
#ifndef NDEBUG
  if (dim < 1)
    SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim < 1");
  if (dim > 3)
    SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim > 3");
  if (p < 0)
    SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "p < 0");
#endif // NDEBUG
  L[0] = 1;
  if (diffL != NULL) {
    diffL[0 * (p + 1) + 0] = 0;
    if (dim >= 2) {
      diffL[1 * (p + 1) + 0] = 0;
      if (dim == 3) {
        diffL[2 * (p + 1) + 0] = 0;
      }
    }
  }
  if (p == 0)
    MoFEMFunctionReturnHot(0);
  L[1] = 2 * x - t + alpha * x;
  if (diffL != NULL) {
#ifndef NDEBUG
    if (diff_x == NULL) {
      SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "diff_s == NULL");
    }
#endif // NDEBUG
    double d_t = (diff_t) ? diff_t[0] : 0;
    diffL[0 * (p + 1) + 1] = (2 + alpha) * diff_x[0] - d_t;
    if (dim >= 2) {
      double d_t = (diff_t) ? diff_t[1] : 0;
      diffL[1 * (p + 1) + 1] = (2 + alpha) * diff_x[1] - d_t;
      if (dim == 3) {
        double d_t = (diff_t) ? diff_t[2] : 0;
        diffL[2 * (p + 1) + 1] = (2 + alpha) * diff_x[2] - d_t;
      }
    }
  }
  if (p == 1)
    MoFEMFunctionReturnHot(0);
  int l = 1;
  for (; l < p; l++) {
    int lp1 = l + 1;
    double a = 2 * lp1 * (lp1 + alpha) * (2 * lp1 + alpha - 2);
    double b = 2 * lp1 + alpha - 1;
    double c = (2 * lp1 + alpha) * (2 * lp1 + alpha - 2);
    double d = 2 * (lp1 + alpha - 1) * (lp1 - 1) * (2 * lp1 + alpha);
    double A = b * (c * (2 * x - t) + alpha * alpha * t) / a;
    double B = d * t * t / a;
    L[lp1] = A * L[l] - B * L[l - 1];
    if (diffL != NULL) {
      double d_t = (diff_t) ? diff_t[0] : 0;
      double diffA = b * (c * (2 * diff_x[0] - d_t) + alpha * alpha * d_t) / a;
      double diffB = d * 2 * t * d_t / a;
      diffL[0 * (p + 1) + lp1] = A * diffL[0 * (p + 1) + l] -
                                 B * diffL[0 * (p + 1) + l - 1] + diffA * L[l] -
                                 diffB * L[l - 1];
      if (dim >= 2) {
        double d_t = (diff_t) ? diff_t[1] : 0;
        double diffA =
            b * (c * (2 * diff_x[1] - d_t) + alpha * alpha * d_t) / a;
        double diffB = d * 2 * t * d_t / a;
        diffL[1 * (p + 1) + lp1] = A * diffL[1 * (p + 1) + l] -
                                   B * diffL[1 * (p + 1) + l - 1] +
                                   diffA * L[l] - diffB * L[l - 1];
        if (dim == 3) {
          double d_t = (diff_t) ? diff_t[2] : 0;
          double diffA =
              b * (c * (2 * diff_x[2] - d_t) + alpha * alpha * d_t) / a;
          double diffB = d * 2 * t * d_t / a;
          diffL[2 * (p + 1) + lp1] = A * diffL[2 * (p + 1) + l] -
                                     B * diffL[2 * (p + 1) + l - 1] +
                                     diffA * L[l] - diffB * L[l - 1];
        }
      }
    }
  }
  MoFEMFunctionReturnHot(0);
}

Variable Documentation

f_phi

double(* f_phi[])(double x)

static

Initial value:

= {f_phi0, f_phi1, f_phi2, f_phi3, f_phi4,
                                      f_phi5, f_phi6, f_phi7, f_phi8, f_phi9}

Definition at line 261 of file base_functions.c.

f_phix

double(* f_phix[])(double x)

static

Initial value:

= {f_phi0x, f_phi1x, f_phi2x, f_phi3x,
                                       f_phi4x, f_phi5x, f_phi6x, f_phi7x,
                                       f_phi8x, f_phi9x}

Definition at line 275 of file base_functions.c.

ierr

PetscErrorCode ierr

static

Definition at line 13 of file base_functions.c.