Approximations

Contains various approximations for differential operators using monomials, RBFs, ... More...

Classes
class	mm::Gaussian< scal_t >
	Gaussian Radial Basis Function. More...
class	mm::InverseMultiquadric< scal_t >
	Inverse Multiquadric Radial Basis Function. More...
class	mm::JacobiSVDWrapper< scalar_t, QRPreconditioner >
	Extends Eigen's JacobiSVD to compute thin U and thin V by default. More...
class	mm::Monomials< vec_t >
	A class representing Monomial basis. More...
class	mm::Multiquadric< scal_t >
	Multiquadric Radial Basis Function. More...
struct	mm::Operator< Derived >
	Base class for a differential operator. More...
struct	mm::Lap< dimension >
	Represents the Laplacian operator. More...
struct	mm::Der1s< dimension >
	Represents a family of all first derivatives. More...
struct	mm::Der2s< dimension >
	Represents a family of all second derivatives. More...
struct	mm::Der1< dimension >
	Represents a first derivative wrt. var. More...
struct	mm::Der2< dimension >
	Represents a second derivative wrt. var1 and var2. More...
struct	mm::Derivative< dimension >
	Represents a general derivative \(\frac{\partial^{|\alpha|}}{\partial x^\alpha}\). More...
class	mm::Polyharmonic< scal_t, k >
	Polyharmonic Radial Basis Function of odd order. More...
class	mm::RBFBasis< RBFType, vec_t >
	Represents a basis of Radial Basis Functions over a local neighbourhood. More...
class	mm::RBFFD< RBFType, vec_t, scale_t, solver_t >
	Computes a RBF-FD approximation of given operator over local neighbourhood. More...
class	mm::ScaleToClosest
	Scale function that scales to the closest neighbor. More...
class	mm::ScaleToFarthest
	Scale function that scales to the farthest neighbor. More...
class	mm::NoScale
	Scale function that indicates no scaling is performed. More...
class	mm::NoWeight< vec_t >
	Class representing no weight function, i.e. a constant 1. More...
class	mm::RBFWeight< RBFType, vec_t >
	Represents a weight function constructed from a Radial Basis function. More...
class	mm::WLS< basis_t, weight_t, scale_t, solver_t >
	A class for generating approximations using Weighted Least Squares over local neighborhoods. More...

Detailed Description

Contains various approximations for differential operators using monomials, RBFs, ...

This is one of the core parts of the library, which supports defining approximations for partial differential operators. Many strong form meshless methods can be implemented this way, such as RBF-FD, DAM, MLSM, GFD, FDM, LRBFCM, DLSM, ...

Approximations are modular and can be easily changed, from basis functions, weight functions, scaling, solvers, RBFs, stencil size, etc...

More about this can be read on the Concepts page.