Boundary integral operators¶

IBoundaryIntegralOperator¶

class pcm::IBoundaryIntegralOperator¶

Subclassed by pcm::bi_operators::Collocation, pcm::bi_operators::Numerical, pcm::bi_operators::Purisima

Public Functions

Eigen::MatrixXd computeS(const ICavity &cav, const IGreensFunction &gf) const¶

Computes the matrix representation of the single layer operator

Parameters

[in] cav: the discretized cavity
[in] gf: a Green’s function

Eigen::MatrixXd computeD(const ICavity &cav, const IGreensFunction &gf) const¶

Computes the matrix representation of the double layer operator

Parameters

[in] cav: the discretized cavity
[in] gf: a Green’s function

Private Functions

Eigen::MatrixXd computeS_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const = 0¶

Computes the matrix representation of the single layer operator

Parameters

[in] elems: list of finite elements of the discretized cavity
[in] gf: a Green’s function

Eigen::MatrixXd computeD_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const = 0¶

Computes the matrix representation of the double layer operator

Parameters

[in] elems: list of finite elements of the discretized cavity
[in] gf: a Green’s function

Collocation¶

class pcm::bi_operators::Collocation : public pcm::IBoundaryIntegralOperator ¶

Implementation of the single and double layer operators matrix representation using one-point collocation.

Calculates the diagonal elements of S as:

\[ S_{ii} = factor * \sqrt{\frac{4\pi}{a_i}} \]

while the diagonal elements of D are:

\[ D_{ii} = -factor * \sqrt{\frac{\pi}{a_i}} \frac{1}{R_I} \]

Author: Roberto Di Remigio
Date: 2015, 2016

Private Functions

Eigen::MatrixXd computeS_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const override¶

Computes the matrix representation of the single layer operator

Parameters

[in] elems: list of finite elements of the discretized cavity
[in] gf: a Green’s function

Eigen::MatrixXd computeD_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const override¶

Computes the matrix representation of the double layer operator

Parameters

[in] elems: list of finite elements of the discretized cavity
[in] gf: a Green’s function

Private Members

double factor_¶: Scaling factor for the diagonal elements of the matrix representation of the S and D operators

Purisima¶

class pcm::bi_operators::Purisima : public pcm::IBoundaryIntegralOperator ¶

Implementation of the double layer operator matrix representation using one-point collocation and Purisima’s strategy for the diagonal of D.

Calculates the diagonal elements of D as:

\[ D_{ii} = -\left(2\pi + \sum_{j\neq i}D_{ij}a_j \right)\frac{1}{a_i} \]

The original reference is [5]

Author: Roberto Di Remigio
Date: 2015, 2016

Private Functions

Eigen::MatrixXd computeS_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const override¶

Computes the matrix representation of the single layer operator

Parameters

[in] elems: list of finite elements of the discretized cavity
[in] gf: a Green’s function

Eigen::MatrixXd computeD_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const override¶

Computes the matrix representation of the double layer operator by collocation using the Purisima sum rule to compute the diagonal elements.

The sum rule for the diagonal elements is:

\[ D_{ii} = -\left(2\pi + \sum_{j\neq i}D_{ij}a_j \right)\frac{1}{a_i} \]

Parameters

[in] elems: discretized cavity
[in] gf: a Green’s function

Private Members

double factor_¶: Scaling factor for the diagonal elements of the matrix representation of the S operator

Numerical¶

class pcm::bi_operators::Numerical : public pcm::IBoundaryIntegralOperator ¶

Implementation of the single and double layer operators matrix representation using one-point collocation.

Calculates the diagonal elements of S and D by collocation, using numerical integration.

Author: Roberto Di Remigio
Date: 2015, 2016

Private Functions

Eigen::MatrixXd computeS_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const override¶

Computes the matrix representation of the single layer operator

Parameters

[in] elems: list of finite elements of the discretized cavity
[in] gf: a Green’s function

Eigen::MatrixXd computeD_impl(const std::vector<cavity::Element> &elems, const IGreensFunction &gf) const override¶

Computes the matrix representation of the double layer operator

Parameters

[in] elems: list of finite elements of the discretized cavity
[in] gf: a Green’s function