artisynth.core.femmodels

Class FemFieldApproximation

java.lang.Object

artisynth.core.femmodels.FemFieldApproximation

public class FemFieldApproximation
extends java.lang.Object

Computes values in order to best approximate a field within a finite element

Constructor Summary

Constructors

Constructor and Description
FemFieldApproximation(FemElementSampler sampler)

Method Summary

Modifier and Type	Method and Description
void	computeIntegralIPointValues(FemElement3d elem, Function3x1 func, VectorNd out) Computes best-fitting coefficients {w_i} to minimize the error between shape-function integrals: E = ||int_x f(x)\phi_i(x)dx - \hat{g}||^2, where \hat{g} = \sum_j w_i p_i(x_j)*\phi_j(x_j)|dx/dX|(x) is the discretized integral of f(x)\phi_j(x) using the element's quadrature rules.
void	computeIntegralNodeValues(FemElement3d elem, Function3x1 func, VectorNd out) Computes best-fitting coefficients {w_i} to minimize the error between shape-function integrals: E = ||int_x f(x)\phi_i(x)dx - int_x \hat{f}(x)\phi_i(x)dx||^2, where \hat{f}(x) = \sum_j w_i \phi_j(x) interpolates the target function according to the FEM shape functions.
void	computeLeastSquaresNodeValues(FemElement3d elem, Function3x1 func, VectorNd out) Computes best-fitting coefficients {w_i} to minimize the least squared error \sum_i ||f(x_i) - \hat{f}(x_i)||^2, where \hat{f}(x) = \sum_j w_i \phi_j(x) interpolates the target function according to the FEM shape functions
MatrixNd	computeMassMatrix(FemElement3d elem)
void	setIntegrationLimits(int minSamples, int maxSamples, double maxVariance)
void	setNumLSQSamples(int n) Number of samples to use when approximating function with least-squares
void	setSampler(FemElementSampler sampler)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

FemFieldApproximation

public FemFieldApproximation(FemElementSampler sampler)

Method Detail

setNumLSQSamples

public void setNumLSQSamples(int n)

Number of samples to use when approximating function with least-squares

Parameters:

n - samples

setSampler

public void setSampler(FemElementSampler sampler)

setIntegrationLimits

public void setIntegrationLimits(int minSamples,
                                 int maxSamples,
                                 double maxVariance)

computeLeastSquaresNodeValues

public void computeLeastSquaresNodeValues(FemElement3d elem,
                                          Function3x1 func,
                                          VectorNd out)

Computes best-fitting coefficients {w_i} to minimize the least squared error \sum_i ||f(x_i) - \hat{f}(x_i)||^2, where \hat{f}(x) = \sum_j w_i \phi_j(x) interpolates the target function according to the FEM shape functions

Parameters:

elem - element to fit

func - function to fit

out - node values

computeMassMatrix

public MatrixNd computeMassMatrix(FemElement3d elem)

computeIntegralNodeValues

public void computeIntegralNodeValues(FemElement3d elem,
                                      Function3x1 func,
                                      VectorNd out)

Computes best-fitting coefficients {w_i} to minimize the error between shape-function integrals: E = ||int_x f(x)\phi_i(x)dx - int_x \hat{f}(x)\phi_i(x)dx||^2, where \hat{f}(x) = \sum_j w_i \phi_j(x) interpolates the target function according to the FEM shape functions.

Parameters:

elem - element to evaluate

func - function to fit

out - node values

computeIntegralIPointValues

public void computeIntegralIPointValues(FemElement3d elem,
                                        Function3x1 func,
                                        VectorNd out)

Computes best-fitting coefficients {w_i} to minimize the error between shape-function integrals: E = ||int_x f(x)\phi_i(x)dx - \hat{g}||^2, where \hat{g} = \sum_j w_i p_i(x_j)*\phi_j(x_j)|dx/dX|(x) is the discretized integral of f(x)\phi_j(x) using the element's quadrature rules. This method requires that there be at least as many shape functions (i.e. nodes) as integration points.

Parameters:

elem - element to consider

func - function to approximate

out - ipnt values