v0.14.0
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Classes | Functions
Base functions

Calculation of base functions at integration points. More...

Collaboration diagram for Base functions:

Classes

struct  MoFEM::BaseFunctionCtx
 Base class used to exchange data between element data structures and class calculating base functions. More...
 
struct  MoFEM::BaseFunction
 Base class if inherited used to calculate base functions. More...
 
struct  MoFEM::EdgePolynomialBase
 Calculate base functions on tetrahedral. More...
 
struct  MoFEM::EntPolynomialBaseCtx
 Class used to pass element data to calculate base functions on tet,triangle,edge. More...
 
struct  MoFEM::FatPrismPolynomialBaseCtx
 Class used to pass element data to calculate base functions on fat prism. More...
 
struct  MoFEM::FatPrismPolynomialBase
 Calculate base functions on tetrahedralFIXME: Need moab and mofem finite element structure to work (that not perfect) More...
 
struct  MoFEM::FlatPrismPolynomialBaseCtx
 Class used to pass element data to calculate base functions on flat prism. More...
 
struct  MoFEM::FlatPrismPolynomialBase
 Calculate base functions on tetrahedralFIXME: Need moab and mofem finite element structure to work (that not perfect) More...
 
struct  MoFEM::HexPolynomialBase
 Calculate base functions on tetrahedral. More...
 
struct  MoFEM::JacobiPolynomialCtx
 Class used to give arguments to Legendre base functions. More...
 
struct  MoFEM::JacobiPolynomial
 Calculating Legendre base functions. More...
 
struct  MoFEM::LegendrePolynomialCtx
 Class used to give arguments to Legendre base functions. More...
 
struct  MoFEM::LegendrePolynomial
 Calculating Legendre base functions. More...
 
struct  MoFEM::LobattoPolynomialCtx
 Class used to give arguments to Lobatto base functions. More...
 
struct  MoFEM::LobattoPolynomial
 Calculating Lobatto base functions. More...
 
struct  MoFEM::KernelLobattoPolynomialCtx
 Class used to give arguments to Kernel Lobatto base functions. More...
 
struct  MoFEM::KernelLobattoPolynomial
 Calculating Lobatto base functions. More...
 
struct  MoFEM::QuadPolynomialBase
 Calculate base functions on triangle. More...
 
struct  MoFEM::TetPolynomialBase
 Calculate base functions on tetrahedral. More...
 
struct  MoFEM::TriPolynomialBase
 Calculate base functions on triangle. More...
 

Functions

PetscErrorCode Legendre_polynomials (int p, double s, double *diff_s, double *L, double *diffL, const int dim)
 Calculate Legendre 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...
 
PetscErrorCode LobattoKernel_polynomials (int p, double s, double *diff_s, double *L, double *diffL, const int dim)
 Calculate Kernel Lobatto base functions. More...
 

Detailed Description

Calculation of base functions at integration points.

Function Documentation

◆ Legendre_polynomials()

PetscErrorCode Legendre_polynomials ( int  p,
double  s,
double diff_s,
double L,
double diffL,
const int  dim 
)

Calculate Legendre approximation basis.

Lagrange polynomial is given by

\[ L_0(s)=1;\quad L_1(s) = s \]

and following terms are generated inductively

\[ L_{l+1}=\frac{2l+1}{l+1}sL_l(s)-\frac{l}{l+1}L_{l-1}(s) \]

Note that:

\[ s\in[-1,1] \quad \textrm{and}\; s=s(\xi_0,\xi_1,\xi_2) \]

where \(\xi_i\) are barycentric coordinates of element.

Parameters
pis approximation order
sis position \(s\in[-1,1]\)
diff_sderivatives of shape functions, i.e. \(\frac{\partial s}{\partial \xi_i}\)
Return values
Lapproximation functions
diffLderivatives, i.e. \(\frac{\partial L}{\partial \xi_i}\)
Parameters
dimdimension
Returns
error code
Examples
edge_and_bubble_shape_functions_on_quad.cpp.

Definition at line 15 of file base_functions.c.

16 {
18#ifndef NDEBUG
19 if (dim < 1)
20 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim < 1");
21 if (dim > 3)
22 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim > 3");
23 if (p < 0)
24 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "p < 0");
25#endif // NDEBUG
26
27 L[0] = 1;
28 if (diffL != NULL) {
29 for (int d = 0; d != dim; ++d) {
30 diffL[d * (p + 1) + 0] = 0;
31 }
32 }
33 if (p == 0)
35
36 L[1] = s;
37 if (diffL != NULL) {
38#ifndef NDEBUG
39 if (diff_s == NULL) {
40 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "diff_s == NULL");
41 }
42#endif // NDEBUG
43 for (int d = 0; d != dim; ++d) {
44 diffL[d * (p + 1) + 1] = diff_s[d];
45 }
46 }
47 if (p == 1)
49
50 int l = 1;
51 for (; l < p; l++) {
52 double A = ((2 * (double)l + 1) / ((double)l + 1));
53 double B = ((double)l / ((double)l + 1));
54 L[l + 1] = A * s * L[l] - B * L[l - 1];
55 if (diffL != NULL) {
56 for (int d = 0; d != dim; ++d) {
57 diffL[d * (p + 1) + l + 1] =
58 A * (diff_s[d] * L[l] + s * diffL[d * (p + 1) + l]) -
59 B * diffL[d * (p + 1) + l - 1];
60 }
61 }
62 }
63
65}
static Index< 'L', 3 > L
static Index< 'p', 3 > p
#define MoFEMFunctionReturnHot(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:447
@ MOFEM_INVALID_DATA
Definition: definitions.h:36
#define MoFEMFunctionBeginHot
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:440
const int dim
FTensor::Index< 'l', 3 > l
float d
Definition: sdf_hertz.py:5
constexpr AssemblyType A

◆ Lobatto_polynomials()

PetscErrorCode Lobatto_polynomials ( int  p,
double  s,
double diff_s,
double L,
double diffL,
const int  dim 
)

Calculate Lobatto base functions [29].

Order of first function is 2 and goes to p.

Parameters
pis approximation order
sis a mapping of coordinates of edge to \([-1, 1]\), i.e., \(s(\xi_1,\cdot,\xi_{dim})\in[-1,1]\)
diff_sjacobian of the transformation, i.e. \(\frac{\partial s}{\partial \xi_i}\)
  • output
Return values
Lvalues basis functions at s
diffLderivatives of basis functions at s, i.e. \(\frac{\partial L}{\partial \xi_i}\)
Parameters
dimdimension
Returns
error code

Definition at line 199 of file base_functions.c.

200 {
201
203#ifndef NDEBUG
204 if (dim < 1)
205 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim < 1");
206 if (dim > 3)
207 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim > 3");
208 if (p < 2)
209 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "p < 2");
210#endif // NDEBUG
211 double l[p + 1];
212 ierr = Legendre_polynomials(p, s, NULL, l, NULL, 1);
213 CHKERRQ(ierr);
214
215 L[0] = 1;
216 if (diffL != NULL) {
217 for (int d = 0; d != dim; ++d) {
218 diffL[d * (p + 1) + 0] = 0;
219 }
220 }
221 L[1] = s;
222 if (diffL != NULL) {
223#ifndef NDEBUG
224 if (diff_s == NULL) {
225 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "diff_s == NULL");
226 }
227#endif // NDEBUG
228 for (int d = 0; d != dim; ++d) {
229 diffL[d * (p + 1) + 1] = diff_s[d];
230 }
231 }
232
233 // Integrated Legendre
234 for (int k = 2; k <= p; k++) {
235 const double factor = 2 * (2 * k - 1);
236 L[k] = 1.0 / factor * (l[k] - l[k - 2]);
237 }
238
239 if (diffL != NULL) {
240 for (int k = 2; k <= p; k++) {
241 double a = l[k - 1] / 2.;
242 for (int d = 0; d != dim; ++d) {
243 diffL[d * (p + 1) + k] = a * diff_s[d];
244 }
245 }
246 }
248}
constexpr double a
static PetscErrorCode ierr
PetscErrorCode Legendre_polynomials(int p, double s, double *diff_s, double *L, double *diffL, const int dim)
Calculate Legendre approximation basis.
FTensor::Index< 'k', 3 > k

◆ LobattoKernel_polynomials()

PetscErrorCode LobattoKernel_polynomials ( int  p,
double  s,
double diff_s,
double L,
double diffL,
const int  dim 
)

Calculate Kernel Lobatto base functions.

This is implemented using definitions from Hermes2d https://github.com/hpfem/hermes following book by Pavel Solin et al [solin2003higher].

Parameters
pis approximation order
sis position \(s\in[-1,1]\)
diff_sderivatives of shape functions, i.e. \(\frac{\partial s}{\partial \xi_i}\)
Return values
Lapproximation functions
diffLderivatives, i.e. \(\frac{\partial L}{\partial \xi_i}\)
Parameters
dimdimension
Returns
error code

Definition at line 345 of file base_functions.c.

347 {
349#ifndef NDEBUG
350 if (dim < 1)
351 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim < 1");
352 if (dim > 3)
353 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "dim > 3");
354 if (p < 0)
355 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "p < 0");
356 if (p > 9)
357 SETERRQ(PETSC_COMM_SELF, MOFEM_NOT_IMPLEMENTED,
358 "Polynomial beyond order 9 is not implemented");
359#endif // NDEBUG
360 if (L) {
361 int l = 0;
362 for (; l != p + 1; l++) {
363 L[l] = f_phi[l](s);
364 }
365 }
366 if (diffL != NULL) {
367#ifndef NDEBUG
368 if (diff_s == NULL) {
369 SETERRQ(PETSC_COMM_SELF, MOFEM_INVALID_DATA, "diff_s == NULL");
370 }
371#endif // NDEBUG
372 int l = 0;
373 for (; l != p + 1; l++) {
374 double a = f_phix[l](s);
375 diffL[0 * (p + 1) + l] = diff_s[0] * a;
376 if (dim >= 2) {
377 diffL[1 * (p + 1) + l] = diff_s[1] * a;
378 if (dim == 3) {
379 diffL[2 * (p + 1) + l] = diff_s[2] * a;
380 }
381 }
382 }
383 }
385}
static double(* f_phi[])(double x)
static double(* f_phix[])(double x)
@ MOFEM_NOT_IMPLEMENTED
Definition: definitions.h:32