A fourth order Runge-Kutta type of exponential time differencing and triangular spectral element method for two dimensional nonlinear Maxwell's equations
DOI10.1016/j.apnum.2024.09.008MaRDI QIDQ6646518
Publication date: 2 December 2024
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
contour integralMaxwell's equationsfourth-order Runge-Kutta methodexponential time differencingtriangular spectral element methodnonlinear conductivity
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Maxwell equations (35Q61)
Cites Work
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- Efficient low-storage Runge-Kutta schemes with optimized stability regions
- Exponential time differencing for stiff systems
- Generalized integrating factor methods for stiff PDEs
- A spectral element method for fluid dynamics: Laminar flow in a channel expansion
- On a singular limit problem for nonlinear Maxwell's equations
- Plane wave discontinuous Galerkin methods for the Helmholtz equation and Maxwell equations in anisotropic media
- An approach to solving Maxwell's equations in time domain
- A time-domain finite element scheme and its analysis for nonlinear Maxwell's equations in Kerr media
- A space-time spectral method for the 1-D Maxwell equation
- High-order accurate schemes for Maxwell's equations with nonlinear active media and material interfaces
- On the efficiency of 5(4) RK-embedded pairs with high order compact scheme and Robin boundary condition for options valuation
- Embedded pairs for optimal explicit strong stability preserving Runge-Kutta methods
- The Crank-Nicolson mixed finite element method for the improved system of time-domain Maxwell's equations
- A second order numerical scheme for nonlinear Maxwell's equations using conforming finite element
- Numerical analysis of a leapfrog ADI-FDTD method for Maxwell's equations in lossy media
- The splitting finite-difference time-domain methods for Maxwell's equations in two dimensions
- Energy-conserved splitting FDTD methods for Maxwell's equations
- Energy-conserved splitting spectral methods for two dimensional Maxwell's equations
- Fast, low-memory numerical methods for radiative transfer via \(hp\)-adaptive mesh refinement
- Convergence of the mixed finite element method for Maxwell's equations with nonlinear conductivity
- Energy-Conserved Splitting Finite-Difference Time-Domain Methods for Maxwell's Equations in Three Dimensions
- Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
- Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
- Symplectic discretization for spectral element solution of Maxwell's equations
- Fourth-Order Time-Stepping for Stiff PDEs
- Discontinuous Galerkin sparse grids methods for time domain Maxwell's equations
- Legendre-tau Chebyshev collocation spectral element method for Maxwell's equations with material interfaces of two dimensional transverse magnetic mode
- An operator splitting Legendre-tau spectral method for Maxwell's equations with nonlinear conductivity in two dimensions
- Explicit high-order exponential time integrator for discontinuous Galerkin solution of Maxwell's equations
- An \textit{hp} finite element method for a two-dimensional singularly perturbed boundary value problem with two small parameters
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