Maxwell solver
GEMPIC.Maxwell1DFEM
— Typemaxwell_solver = MaxwellFEM1D( mesh, degree )
1D Maxwell spline finite element solver on a periodic grid
Lx
: length of Periodic domaindelta_x
: cell sizen_dofs
: number of cells (and grid points)s_deg_0
: spline degree 0-formss_deg_1
: spline degree 1-formsmass_0
: coefficients of 0-form mass matrixmass_1
: coefficients of 1-form mass matrixeig_mass0
: eigenvalues of circulant 0-form mass matrixeig_mass1
: eigenvalues of circulant 1-form mass matrixeig_weak_ampere
: eigenvalues of circulant update matrix for Ampereeig_weak_poisson
: eigenvalues of circulant update matrix for Poissonplan_fw
: fft plan (forward)plan_bw
: fft plan (backward)
GEMPIC.compute_b_from_e!
— Methodcompute_b_from_e!( field_out, maxwell_solver, delta_t, field_in)
Compute Bz from Ey using strong 1D Faraday equation for spline coefficients
\[B_z^{new}(x_j) = B_z^{old}(x_j) - \frac{\Delta t}{\Delta x} (E_y(x_j) - E_y(x_{j-1})\]
GEMPIC.compute_e_from_b!
— Methodcompute_e_from_b!(field_out, maxwell_solver, delta_t, field_in)
compute Ey from Bz using weak Ampere formulation
GEMPIC.compute_e_from_j!
— Methodcompute_e_from_j!(e, maxwell_solver, current, component)
Compute $E_i$ from $j_i$ integrated over the time interval using weak Ampere formulation
GEMPIC.compute_rhs_from_function!
— Methodcomputerhsfromfunction(self, func, degree, coefsdofs)
Compute the FEM right-hand-side for a given function f and periodic splines of given degree.
Its components are $\int f N_i dx$ where $N_i$ is the B-spline starting at $x_i$.
GEMPIC.inner_product
— Methodinner_product( maxwell_solver, coefs1_dofs, coefs2_dofs, degree )
maxwell_solver
: Maxwell solver objectcoefs1_dofs
: Coefficient for each DoFcoefs2_dofs
: Coefficient for each DoF- `degree : Specify the degree of the basis functions
return squared L2 norm
GEMPIC.l2norm_squared
— Methodl2norm_squared(maxwell_solver, coefs_dofs, degree)
Compute square of the L2norm
GEMPIC.l2norm_squared2
— Methodl2norm_squared(maxwell_solver, coefs_dofs, degree)
Compute square of the L2norm
GEMPIC.l2projection!
— Methodl2projection!(coefs_dofs, maxwell, func, degree)
Compute the L2 projection of a given function f on periodic splines of given degree