/*! \brief Builds the CPCM matrix
* \param[in] cav the discretized cavity
* \param[in] gf_i Green's function inside the cavity
* \param[in] epsilon permittivity outside the cavity
* \param[in] correction CPCM correction factor
* \return the \f$ \mathbf{K} = f(\varepsilon)\mathbf{S}^{-1} \f$ matrix
*
* This function calculates the PCM matrix.
* The matrix is not symmetrized and is not symmetry packed.
*/
inline Eigen::MatrixXd CPCMMatrix(const Cavity & cav, const IGreensFunction & gf_i, double epsilon, double correction)
{
// The total size of the cavity
size_t cavitySize = cav.size();
// The number of irreps in the group
int nrBlocks = cav.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cav.irreducible_size();
// Compute SI and DI on the whole cavity, regardless of symmetry
TIMER_ON("Computing SI");
Eigen::MatrixXd SI = gf_i.singleLayer(cav.elements());
TIMER_OFF("Computing SI");
// Perform symmetry blocking
// If the group is C1 avoid symmetry blocking, we will just pack the fullPCMMatrix
// into "block diagonal" when all other manipulations are done.
if (cav.pointGroup().nrGenerators() != 0) {
TIMER_ON("Symmetry blocking");
symmetryBlocking(SI, cavitySize, dimBlock, nrBlocks);
TIMER_OFF("Symmetry blocking");
}
double fact = (epsilon - 1.0)/(epsilon + correction);
// Invert SI using LU decomposition with full pivoting
// This is a rank-revealing LU decomposition, this allows us
// to test if SI is invertible before attempting to invert it.
Eigen::FullPivLU<Eigen::MatrixXd> SI_LU(SI);
if (!(SI_LU.isInvertible()))
PCMSOLVER_ERROR("SI matrix is not invertible!", BOOST_CURRENT_FUNCTION);
return fact * SI_LU.inverse();
}
/*! \brief Builds the **anisotropic** IEFPCM matrix
* \param[in] cav the discretized cavity
* \param[in] gf_i Green's function inside the cavity
* \param[in] gf_o Green's function outside the cavity
* \return the \f$ \mathbf{K} = \mathbf{T}^{-1}\mathbf{R}\mathbf{A} \f$ matrix
*
* This function calculates the PCM matrix. We use the following definitions:
* \f[
* \begin{align}
* \mathbf{T} &=
* \left(2\pi\mathbf{I} - \mathbf{D}_\mathrm{e}\mathbf{A}\right)\mathbf{S}_\mathrm{i}
* +\mathbf{S}_\mathrm{e}\left(2\pi\mathbf{I} +
* \mathbf{A}\mathbf{D}_\mathrm{i}^\dagger\right) \\
* \mathbf{R} &=
* \left(2\pi\mathbf{A}^{-1} - \mathbf{D}_\mathrm{e}\right) -
* \mathbf{S}_\mathrm{e}\mathbf{S}^{-1}_\mathrm{i}\left(2\pi\mathbf{A}^{-1}-\mathbf{D}_\mathrm{i}\right)
* \end{align}
* \f]
* The matrix is not symmetrized and is not symmetry packed.
*/
inline Eigen::MatrixXd anisotropicIEFMatrix(const Cavity & cav, const IGreensFunction & gf_i, const IGreensFunction & gf_o)
{
// The total size of the cavity
size_t cavitySize = cav.size();
// The number of irreps in the group
int nrBlocks = cav.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cav.irreducible_size();
// Compute SI, DI and SE, DE on the whole cavity, regardless of symmetry
TIMER_ON("Computing SI");
Eigen::MatrixXd SI = gf_i.singleLayer(cav.elements());
TIMER_OFF("Computing SI");
TIMER_ON("Computing DI");
Eigen::MatrixXd DI = gf_i.doubleLayer(cav.elements());
TIMER_OFF("Computing DI");
TIMER_ON("Computing SE");
Eigen::MatrixXd SE = gf_o.singleLayer(cav.elements());
TIMER_OFF("Computing SE");
TIMER_ON("Computing DE");
Eigen::MatrixXd DE = gf_o.doubleLayer(cav.elements());
TIMER_OFF("Computing DE");
// Perform symmetry blocking
// If the group is C1 avoid symmetry blocking, we will just pack the fullPCMMatrix
// into "block diagonal" when all other manipulations are done.
if (cav.pointGroup().nrGenerators() != 0) {
TIMER_ON("Symmetry blocking");
symmetryBlocking(DI, cavitySize, dimBlock, nrBlocks);
symmetryBlocking(SI, cavitySize, dimBlock, nrBlocks);
symmetryBlocking(DE, cavitySize, dimBlock, nrBlocks);
symmetryBlocking(SE, cavitySize, dimBlock, nrBlocks);
TIMER_OFF("Symmetry blocking");
}
Eigen::MatrixXd a = cav.elementArea().asDiagonal();
Eigen::MatrixXd Id = Eigen::MatrixXd::Identity(cavitySize, cavitySize);
// 1. Form T
TIMER_ON("Assemble T matrix");
Eigen::MatrixXd fullPCMMatrix = ((2 * M_PI * Id - DE * a) * SI + SE * (2 * M_PI * Id + a * DI.adjoint().eval()));
TIMER_OFF("Assemble T matrix");
// 2. Invert T using LU decomposition with full pivoting
// This is a rank-revealing LU decomposition, this allows us
// to test if T is invertible before attempting to invert it.
TIMER_ON("Invert T matrix");
Eigen::FullPivLU<Eigen::MatrixXd> T_LU(fullPCMMatrix);
if (!(T_LU.isInvertible())) PCMSOLVER_ERROR("T matrix is not invertible!", BOOST_CURRENT_FUNCTION);
fullPCMMatrix = T_LU.inverse();
TIMER_OFF("Invert T matrix");
Eigen::FullPivLU<Eigen::MatrixXd> SI_LU(SI);
if (!(SI_LU.isInvertible())) PCMSOLVER_ERROR("SI matrix is not invertible!", BOOST_CURRENT_FUNCTION);
TIMER_ON("Assemble T^-1R matrix");
fullPCMMatrix *= ((2 * M_PI * Id - DE * a) - SE * SI_LU.inverse() * (2 * M_PI * Id - DI * a));
TIMER_OFF("Assemble T^-1R matrix");
return fullPCMMatrix;
}
/******** Timer_SetPeriod **************************************************
// Set the interrupt period for Timer
// Input:
// timer - one of the Timer_T value ( Timer1A, Timer1B... )
// period - n of the 20ns time slices
// Output: none
// ------------------------------------------------------------------------*/
void Timer_SetPeriod ( Timer_T timer, unsigned long period )
{
if ( TIMER_ON(timer/2) )
{
// only can set period for timer that has been initialized
TimerLoadSet ( Timer_Base[timer], get_half_timer(timer), period);
}
}
/******** Timer_GetTime ****************************************************
// Get the current value in timer
// Input: timer is one of the Timer_T value ( Timer1A, Timer1B... )
// Output: n of the 20ns time slices.
// Return 0xFFFFFFFF if the timer is not initialized
// ------------------------------------------------------------------------*/
unsigned long Timer_GetTime ( Timer_T timer )
{
if ( TIMER_ON(timer/2) )
{
return TimerValueGet( Timer_Base[timer], get_half_timer(timer) );
}
else
{
return 0xFFFFFFFF;
}
}
/*! \brief Builds the **isotropic** IEFPCM matrix
* \param[in] cav the discretized cavity
* \param[in] gf_i Green's function inside the cavity
* \param[in] epsilon permittivity outside the cavity
* \return the \f$ \mathbf{K} = \mathbf{T}^{-1}\mathbf{R}\mathbf{A} \f$ matrix
*
* This function calculates the PCM matrix. We use the following definitions:
* \f[
* \begin{align}
* \mathbf{T} &=
* \left(2\pi\frac{\varepsilon+1}{\varepsilon-1}\mathbf{I} - \mathbf{D}_\mathrm{i}\mathbf{A}\right)\mathbf{S}_\mathrm{i} \\
* \mathbf{R} &=
* \left(2\pi\mathbf{A}^{-1} - \mathbf{D}_\mathrm{i}\right)
* \end{align}
* \f]
* The matrix is not symmetrized and is not symmetry packed.
*/
inline Eigen::MatrixXd isotropicIEFMatrix(const Cavity & cav, const IGreensFunction & gf_i, double epsilon)
{
// The total size of the cavity
size_t cavitySize = cav.size();
// The number of irreps in the group
int nrBlocks = cav.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cav.irreducible_size();
// Compute SI and DI on the whole cavity, regardless of symmetry
TIMER_ON("Computing SI");
Eigen::MatrixXd SI = gf_i.singleLayer(cav.elements());
TIMER_OFF("Computing SI");
TIMER_ON("Computing DI");
Eigen::MatrixXd DI = gf_i.doubleLayer(cav.elements());
TIMER_OFF("Computing DI");
// Perform symmetry blocking
// If the group is C1 avoid symmetry blocking, we will just pack the fullPCMMatrix
// into "block diagonal" when all other manipulations are done.
if (cav.pointGroup().nrGenerators() != 0) {
TIMER_ON("Symmetry blocking");
symmetryBlocking(DI, cavitySize, dimBlock, nrBlocks);
symmetryBlocking(SI, cavitySize, dimBlock, nrBlocks);
TIMER_OFF("Symmetry blocking");
}
Eigen::MatrixXd a = cav.elementArea().asDiagonal();
Eigen::MatrixXd Id = Eigen::MatrixXd::Identity(cavitySize, cavitySize);
// Tq = -Rv -> q = -(T^-1 * R)v = -Kv
// T = (2 * M_PI * fact * aInv - DI) * a * SI; R = (2 * M_PI * aInv - DI)
// fullPCMMatrix_ = K = T^-1 * R * a
// 1. Form T
double fact = (epsilon + 1.0)/(epsilon - 1.0);
TIMER_ON("Assemble T matrix");
Eigen::MatrixXd fullPCMMatrix = (2 * M_PI * fact * Id - DI * a) * SI;
TIMER_OFF("Assemble T matrix");
// 2. Invert T using LU decomposition with full pivoting
// This is a rank-revealing LU decomposition, this allows us
// to test if T is invertible before attempting to invert it.
TIMER_ON("Invert T matrix");
Eigen::FullPivLU<Eigen::MatrixXd> T_LU(fullPCMMatrix);
if (!(T_LU.isInvertible()))
PCMSOLVER_ERROR("T matrix is not invertible!", BOOST_CURRENT_FUNCTION);
fullPCMMatrix = T_LU.inverse();
TIMER_OFF("Invert T matrix");
// 3. Multiply T^-1 and R
TIMER_ON("Assemble T^-1R matrix");
fullPCMMatrix *= (2 * M_PI * Id - DI * a);
TIMER_OFF("Assemble T^-1R matrix");
return fullPCMMatrix;
}
void CPCMSolver::buildSystemMatrix_impl(const ICavity & cavity,
const IGreensFunction & gf_i,
const IGreensFunction & gf_o,
const IBoundaryIntegralOperator & op) {
if (!isotropic_)
PCMSOLVER_ERROR("C-PCM is defined only for isotropic environments!");
TIMER_ON("Computing S");
double epsilon = gf_o.permittivity();
S_ = op.computeS(cavity, gf_i);
S_ /= (epsilon - 1.0) / (epsilon + correction_);
// Get in Hermitian form
if (hermitivitize_)
utils::hermitivitize(S_);
TIMER_OFF("Computing S");
// Symmetry-pack
// The number of irreps in the group
int nrBlocks = cavity.pointGroup().nrIrrep();
// The size of the irreducible portion of the cavity
int dimBlock = cavity.irreducible_size();
utils::symmetryPacking(blockS_, S_, dimBlock, nrBlocks);
built_ = true;
}
/******** Timer_Init *******************************************************
// Initialize timer as either CCP, PWM or regular timer
// Input:
// timer - one of the Timer_T value ( Timer1A, Timer1B... )
// config - indicates the operational mode of the timer
// xParameter - additional configure value, depends the mode of timer
// tBool - if true then enable timer right away
// Output: none
// ------------------------------------------------------------------------*/
void Timer_Init ( Timer_T timer, Timer_Config config, unsigned long xParameter, tBoolean enable )
{
unsigned long timer_base, timer_config;
// only turn on system control for the same timer once
if ( !(TIMER_ON(timer/2)) )
{
SysCtlPeripheralEnable ( Timer_Periph[timer] );
TIMER_POWER_ON ( timer/2 );
}
// disable timer before configure
TimerDisable ( Timer_Base[timer], get_half_timer(timer) );
// determine what user want this timer to do
switch ( config )
{
case Timer_CCP:
{
if ( timer >= NUM_CCP )
{
// return if the timer does not associate with a CCP pin
return;
}
// initialize CCP pin
GPIO_Init ( CCP_Port[timer], CCP_Pin[timer], 0, 0, CCP );
// initialize Timer
if ( timer % 2 )
{
// timer B, 16bit capture
TimerConfigure ( Timer_Base[timer], TIMER_CFG_16_BIT_PAIR | TIMER_CFG_B_ONE_SHOT | TIMER_CFG_B_CAP_TIME );
TimerControlEvent ( Timer_Base[timer], TIMER_B, xParameter);
Timer_IntFlag[timer] = TIMER_CAPB_EVENT;
}
else
{
// timer A, 16bit capture
TimerConfigure ( Timer_Base[timer], TIMER_CFG_16_BIT_PAIR | TIMER_CFG_A_ONE_SHOT | TIMER_CFG_A_CAP_TIME );
TimerControlEvent ( Timer_Base[timer], TIMER_A, xParameter);
Timer_IntFlag[timer] = TIMER_CAPA_EVENT;
}
break;
}
case Timer_PWM:
{
break;
}
case Timer_Periodic:
{
break;
}
case Timer_OneTime:
{
break;
}
default:
{
break;
}
}
if ( enable )
{
TimerEnable ( Timer_Base[timer], get_half_timer(timer) );
}
}
