Index Symbols | A | B | C | D | E | F | G | H | I | J | L | M | N | O | P | R | S | T | U | V | W Symbols 0), [1], [2] A actual advection equation angle discontinuity B bar magnet best approximation, [1] best approximation error (BAE) Betti number connected components number of holes tunnels or handles voids or cavities bilinear form block matrix in mixed systems in ngsolve solver block vector boundary layer exact solution instability plot branch cut C coboundaries cocycles coefficient functions (CoefficientFunction) coffee grounds cohomologies coil current from voltage magnetic field from current conductivity in electrostatics of copper connected components Betti number conservation law integral form conservative flux definition element-wise conservation single-valued flux control volume conservation law discrete convection-diffusion equation convergence rates apparent numerical order of convergence (NOC) ConvertOperator curl matrix COO() method (ngsolve) coo_matrix (scipy) coupling degrees of freedom of CR space coupling type (CouplingType) Crouzeix-Raviart (CR) space higher order generalization P1-nonconforming space shape functions curl matrix ConvertOperator curl operator in 2D, [1] current density D Darcy law degrees of freedom coupling vs local global DG (discontinuous Galerkin) space 1D 2D DG method the need for differentiation automatic linearization (Variation) of coefficient functions Draw 1D deformation (surface plot) menu options in dict vectors E edge element electrostatics element boundary integrals to compute jump to compute nonconservative flux jump using dx(element_boundary=True) energy lost flux jump estimated evaluating at mesh points F facet finite element space the NormalFacetFESpace class facet shared by two elements flux non-conservative flux flux jump energy lost G gauge constraint glue subdomains sum (+) subdomains gradient grid function (GridFunction) H hat functions, [1] heat flux conductive (Fourier law) convective Fourier's law heated plate I identity matrix in ngsolve preconditioner projector insulator integrate interpolation (canonical) iron magnetic permeability iterative solver J jump of a scalar function of normal component of normal flux of tangential component orientation-independent definition L L-shape singular Maxwell solution L-shaped domain Lagrange multipliers constrained optimization Lagrange space (Courant space) Lagrangian (on finite elements) linear form local degrees of freedom M magnet magnetization curl as distribution discontinuous of ferromagnet magnetostatic potential magnetostatics mask projector Maxwell equations in 2D Maxwell equations in 3D meshing 1D 2D glue vs sum (+) holes in 2D maxh for a point occ (Open Cascade) polygon of n sides single triangle subdomains in 2D, [1] minimization MinRes mixed method assemble big bilinear form assemble blocks Raviart-Thomas N Newton solver Nédélec space for magnetic vector potential for TE & TM global space of Type 1 order=p+1-max(1-p, [1], [2] the HCurl class nonconforming space norm broken Sobolev norm first Sobolev norm Lebesgue norm normal vector facet space (NormalFacetFESpace) number of holes Betti number numerical order of convergence (NOC) convergence rates O Ohm's law optical fiber Oswald approximation vector elements overshoots P pardiso permeability magnetic piecewise constant element by element subdomain by subdomain plotting 1D, [1] bar plot Draw (2D) polar coordinates porous media flow permeability preconditioner block preconditioner for mixed systems pretty table projection L2-orthogonal projector identity mask range set by bits R rank of a matrix scipy.linalg.svdvals Raviart-Thomas space element shape functions global shape functions global space definition the HDiv class re-entrant corner refinement uniform rot operator rotated gradient S scipy.linalg.svdvals rank of a matrix shape functions 1D, [1] 2D Crouzeix-Raviart (nonconforming) element global, [1] Lagrange singular values sparse matrix solver sparsecholesky stationary convection stiffness matrix structure preservation sum (+) subdomains glue subdomains superconvergence conservation divergence of RT interpolant Nédélec interpolant surface field sources T TE (transverse electric) system test function thermal conductivity time-harmonic TM (transverse magnetic) system topological invariants Trace Raviart-Thomas space trial function, [1] tunnels or handles Betti number U umfpack undershoots unstable method V variation voids or cavities Betti number W waveguide weakly imposed boundary condition Whitney forms
