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GemaCoreLib
The GeMA Core library
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GemaCoreLib
The GeMA Core library
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A helper class used to combine 1, 2 or 3 single "line" integration rule tables into a multi-dimensional integration rule. The combined rule has the same number of natural coordinates as the number of supplied tables. Also, each rule parameter corresponds to a table and rule degree. More...
#include <gmIntegrationRule.h>
Public Member Functions | |
| bool | isValid () const |
| Returns true if this is a valid integration rule object, false if not. | |
| virtual int | numPoints () const |
| Returns the number of integration points returned by this rule. | |
| virtual void | integrationPoint (int index, GmVector &naturalCoord, double *weight) const |
| Given an index from 0 to numPoints() - 1, fills naturalCoord and weight with the position and weigth of the given integration point. | |
| virtual int | numNaturalCoord () const |
| Returns the number of natural coordinates used by this integration rule. | |
| virtual int | degree () const |
| Returns the integration degree for this rule (The polynomial degree for which this rule is exact) | |
| virtual GmIntegrationRuleType | ruleType () const |
| Returns the type of the integration rule. | |
| virtual QString | ruleName () const |
| Returns the current ruleName adopted by this integration rule. | |
| virtual int | rulePar (int num) const |
| Returns the value of the numbered rule parameter received in the rule constructor (-1 if unused). Num should be a value between 1 and 3. | |
| virtual int | ruleParNumPoints (int num) const |
| virtual int | cacheKey () const |
| Returns an unique integer that can be used to uniquelly represent this kind of integration rule (i.e, two objects with the same cache key should return exactly the same set of integration points). | |
| void | integrationPoint (int index, GmVector &naturalCoord, double *weight) const |
| This function returns weights and points to be sampled for 1D quadrature integration. | |
| void | integrationPoint (int index, GmVector &naturalCoord, double *weight) const |
| This function returns weights and points to be sampled for 2D quadrature integration over a quadrilateral with axis Xi and Eta. | |
| void | integrationPoint (int index, GmVector &naturalCoord, double *weight) const |
| This function returns weights and points to be sampled for 3D quadrature integration over a hexahedron with axis Xi, Eta and Zeta. | |
 Public Member Functions inherited from GmIntegrationRule | |
| virtual | ~GmIntegrationRule () |
| Virtual destructor. | |
| virtual const QVector< int > & | closestIntegrationIndex (GmCellType type, int P, int Q, int nodeIndex) const |
| Returns a list with the index of the closest(s) integraion points from nodeIndex. | |
Protected Member Functions | |
| GmLinearMultiTableIntegrationRule (GmIntegrationRuleType ruleType, GmIntegrationRuleCacheKeyBase cacheKeyBase, int rule1, const QVector< QPair< double, double > > *table1, int degree1, int rule2=-1, const QVector< QPair< double, double > > *table2=NULL, int degree2=0, int rule3=-1, const QVector< QPair< double, double > > *table3=NULL, int degree3=0) | |
| Constructor. Receives the rule type + cache key base, along with the set of rule numbers + the table defining the integration rule in that dimension. | |
| Protected Member Functions inherited from GmIntegrationRule | |
| int | makeCacheKey (GmIntegrationRuleCacheKeyBase base, bool closed, int rule1, int rule2=-1, int rule3=-1) const |
| Creates an unique cache key based on the rule type cache key and the rule parameters. | |
| QString | makeRuleName (GmIntegrationRuleType irType, int rule1, int rule2=-1, int rule3=-1) const |
| Returns a standard rule name based on rule type and rule parameters. | |
Protected Attributes | |
| GmIntegrationRuleType | _rtype |
| The rule type. | |
| int | _degree |
| The combined rule degree (the minimum of the individual rule degrees) | |
| int | _nip |
| The number of integration points. | |
| int | _rules [3] |
| The rule numbers. -1 if unused. If a rule is -1, all following rules are also -1. | |
| const QVector< QPair< double, double > > * | _tables [3] |
| Tables with point & weight data for the given rule. NULL if unused. If a table is NULL, all following tables are NULL. | |
| GmIntegrationRuleCacheKeyBase | _keyBase |
| The base cache key. | |
Additional Inherited Members | |
| Static Public Member Functions inherited from GmIntegrationRule | |
| static GmIntegrationRule * | instance (GmCellType type, int P, int Q, GmIntegrationRuleType irType, int rule1=-1, int rule2=-1, int rule3=-1) |
| Instanciates an integration rule for the specified element type using the provided parameters. Returns NULL if the parameter set results in an invalid integration rule. | |
A helper class used to combine 1, 2 or 3 single "line" integration rule tables into a multi-dimensional integration rule. The combined rule has the same number of natural coordinates as the number of supplied tables. Also, each rule parameter corresponds to a table and rule degree.
The number of points is equal to the product of the individual table sizes.
The combined rule degree is the minimum of the individual degrees.
The template parameter is the number of tables. It is used so that the integrationPoint() method can be specialized without runtime conditions overhead.
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protected |
Constructor. Receives the rule type + cache key base, along with the set of rule numbers + the table defining the integration rule in that dimension.
Creates an invalid object for rules outside the valid range (table == NULL). See comments on GmIntegrationRule::isValid()
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inlinevirtual |
Returns an unique integer that can be used to uniquelly represent this kind of integration rule (i.e, two objects with the same cache key should return exactly the same set of integration points).
The returned value is used together with an element type as a cache key in closestIntegrationIndex() and in GmShape::gaussExtrapolationMatrix().
Implements GmIntegrationRule.
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inlinevirtual |
Returns the integration degree for this rule (The polynomial degree for which this rule is exact)
Implements GmIntegrationRule.
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virtual |
Given an index from 0 to numPoints() - 1, fills naturalCoord and weight with the position and weigth of the given integration point.
After filled, naturalCoord will be a vector with size equal to numNaturalCoord(), which should be equal to the number of natural coordinates of the shape function of the element that this rule will be tied to.
Implements GmIntegrationRule.
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virtual |
This function returns weights and points to be sampled for 1D quadrature integration.
In 1D, quadrature integration states that the integral from -1 to 1 of F(x) dx is aproximately equal to the sum from i=1 to p of wi * F(xi), where p is the rule number.
See Felippa, chapter 17, eq 17.11 and table 17.1 (pages 17-6 and 17-7) for Gauss rules
| index | Index (i, from 0 to numPoints()-1) of the point to be sampled |
| naturalCoord | Returns the point where the function F should be sampled (xi) |
| weight | Returns the weight of this point (wi) |
Implements GmIntegrationRule.
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virtual |
This function returns weights and points to be sampled for 2D quadrature integration over a quadrilateral with axis Xi and Eta.
In 2D for a quadrilateral, where the function variables are independent, the 2D product rule states that the double integral from -1 to 1 in both variables, Xi and Eta, of F(Xi, Eta) dXi dEta is equal to the sum from i = 1 to p1 of the sum from j = 1 to p2 of wi * wj * F(Xii, Etaj), where p1 is the quadrature rule number in the Xi direction and p2 the rule number in the Eta direction.
See Felippa, chapter 17, eq 17.15 (page 17-8) for Gauss rules.
| index | Index (i, from 0 to numPoints()-1) of the point to be sampled |
| naturalCoord | Returns the point where the function F should be sampled (Xii, Etaj) |
| weight | Returns the weight of this point (wi * wj) |
Implements GmIntegrationRule.
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virtual |
This function returns weights and points to be sampled for 3D quadrature integration over a hexahedron with axis Xi, Eta and Zeta.
In 3D for a hexahedron, where the function variables are independent, the 3D product rule states that the triple integral from -1 to 1 in all variables, Xi, Eta and Zeta, of F(Xi, Eta, Zeta) dXi dEta dZeta is equal to the sum from i = 1 to p1 of the sum from j = 1 to p2 of the sum from k = 1 to p3 of wi * wj * wk * F(Xii, Etaj, Zetak), where p1 is the quadrature rule number in the Xi direction, p2 the rule number in the Eta direction and p3 the rule number in the Zeta direction.
| index | Index (i, from 0 to numPoints()-1) of the point to be sampled |
| naturalCoord | Returns the point where the function F should be sampled (Xii, Etaj, Zetak) |
| weight | Returns the weight of this point (wi * wj * wk) |
Implements GmIntegrationRule.
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inlinevirtual |
Returns true if this is a valid integration rule object, false if not.
An invalid object can be created when an invalid rule number is passed to the constructor of an integration rule. The result of calling a method other then isValid() over an invalid integration rule is undefined.
Implements GmIntegrationRule.
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inlinevirtual |
Returns the number of natural coordinates used by this integration rule.
Implements GmIntegrationRule.
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inlinevirtual |
Returns the number of integration points returned by this rule.
Implements GmIntegrationRule.
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inlinevirtual |
Returns the current ruleName adopted by this integration rule.
Implements GmIntegrationRule.
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inlinevirtual |
Returns the value of the numbered rule parameter received in the rule constructor (-1 if unused). Num should be a value between 1 and 3.
Implements GmIntegrationRule.
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inlinevirtual |
Returns the number of integration points associated with the given rule parameter. This is useful for compound rules to access the number of points in each "dimension". For non compound rules, returns the number of points. Keep in mind that following the rulePar way, it returns -1 for a unknown parameter. In a 2 x 3 quad rule, for example, it should return 2 for parameter 0 and 3 for parameter 1. This method is necessary since for Newton Coates rules for tri/tet elements the number of points is NOT equal to the parameter and when combined in a Wedge this information is necessary.
Implements GmIntegrationRule.
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inlinevirtual |
Returns the type of the integration rule.
Implements GmIntegrationRule.
1.12.0