Core module

Detailed Description

The Core module is the backbone of the library. Here an abstract interface is defined for a gsBasis, that is, a set of real-valued functions living on a parameter domain. At this level, we do not specify how these functions (or its derivatives) should be evaluated. However, a number of virtual member functions define an interface that should be implemented by derived classes of this type. Another abstract class is the gsGeometry class. This object consists of a (still abstract) basis and a coefficient vector, and represents a patch. Note that parameter or physical dimension are not specified at this point. There are four classes directly derived from the geometry class; these are gsCurve, gsSurface, gsVolume and gsBulk. These are parametric objects with known parameter space dimension 1 ,2, 3, and 4 respectively.

Another abstract class is the gsFunction class. The interface for this class includes evaluation, derivations and other related operations. The gsGgeometry abstract class is actually deriving from the function class, demonstrating the fact that parametric geometries can be simply viewed as (vector) functions. Another interesting object is the gsMultipatch object. CAD models are composed of many patches. Therefore, a multipatch structure is of great importance. It contains two types of information; first, geometric information, essentially a list of geometry patches. Second, the gsBoxTopology class (inherited by gsMultiPatch) captures topological information between the patches, that is, the adjacency graph between patch boundaries, degenerate points, and so on. Let us also mention the gsField class, which is the object that typically represents the solution of a PDE. A gsField is a mathematical scalar or vector field which is defined on a parametric patch, or multipatch object. It may be evaluated either on the parameter or physical space, as the isogeometric paradigm suggests.

See Geometries hierarchy and Bases hierarchy.

Namespaces
	gismo::math
	This namespace contains common mathematical functions.
	gismo::memory
	This namespace contains functions related to memory management.

Classes
struct	boundary
	Struct that defines the boundary sides and corners and types of a geometric object. More...
class	gsAbsError< T >
	Generates a field with value the absolute difference (error) between and isogeometric function and a function defined on the physical domain. More...
class	gsAffineFunction< T >
	Representation of an affine function. More...
class	gsBasis< T >
	A basis represents a family of scalar basis functions defined over a common parameter domain. More...
class	gsBasisFun< T >
	Represents an individual function in a function set, or a certain component of a vector-valued function. More...
class	gsBasisRefs< T >
	Simple class to hold a list of gsBasis which discretize a PDE system on a given patch. More...
class	gsBoxTopology
	Defines a topological arrangement of a collection of "boxes" (e.g., parameter domains that map to physical-domain patches). More...
class	gsBulk< T >
	Abstract base class representing a 4D bulk. More...
class	gsConstantBasis< T >
	Class defining a dummy basis of constant functions. This is used for compatibility reasons. More...
class	gsConstantFunction< T >
	Class defining a globally constant function. More...
class	gsCurve< T >
	Abstract base class representing a curve. More...
class	gsDofMapper
	Maintains a mapping from patch-local dofs to global dof indices and allows the elimination of individual dofs. More...
class	gsDomain< T >
	Class representing a domain. i.e. a collection of elements (triangles, rectangles, cubes, simplices. More...
class	gsDomainIterator< T >
	Class which enables iteration over all elements of a parameter domain. More...
class	gsField< T >
	A scalar of vector field defined on a m_parametric geometry. More...
struct	gsFieldCreator< T >
	Class that creates standard fields on a given parametric (multipatch) geometry. More...
class	gsFuncCoordinate< T >
	Represents a certain component of a vector-valued function. More...
class	gsFunction< T >
	A function \(f:\mathbb{R}^n\rightarrow\mathbb{R}^m\) from a n-dimensional domain to an m-dimensional image. More...
class	gsFunctionExpr< T >
	Class defining a multivariate (real or vector) function given by a string mathematical expression. More...
class	gsGeometry< T >
	Abstract base class representing a geometry map. More...
class	gsGeometryTransform< T >
	Representation of a transformed geometry. More...
class	gsGradientField< T >
	Generates a field with value being the gradient of an isogeometric function. More...
class	gsJacDetField< T >
	Generates a field with value the Jacobian determinant of a geometry. More...
class	gsMultiBasis< T >
	Holds a set of patch-wise bases and their topology information. More...
class	gsMultiPatch< T >
	Container class for a set of geometry patches and their topology, that is, the interface connections and outer boundary faces. More...
class	gsNormalField< T >
	Generates the normal field of a geometry. More...
class	gsParamField< T >
	Generates a field that attaches the parameter values on each physical point. More...
class	gsPatchIdField< T >
	Generates a field that indicates the boundary sides on the geometry. More...
class	gsPatchwiseFunction< T >
	A function depending on an index i, typically referring to a patch/sub-domain. More...
class	gsPiecewiseFunction< T >
	A function depending on an index i, typically referring to a patch/sub-domain. On each patch a different gsFunction object is used. More...
class	gsRationalBasis< SrcT >
	Class that creates a rational counterpart for a given basis. More...
class	gsStdVectorRef< obj >
	Simple wrapper class for a vector of objects. More...
class	gsSurface< T >
	Abstract base class representing a surface. More...
class	gsVolume< T >
	Provides declaration of Volume abstract interface. More...