On hybrid temporal basis functions for stable numerical solution of time domain boundary integral equations

Burton A, Miller G (1971) The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc R Soc Lond A 323(1553):201–210.

Morino L (2003) Is there a difference between aeroacoustics and aerodynamics? An aeroelastician’s viewpoint. AIAA J 41(7):1209–1223.

Chappell D, Harris P, Henwood D, Chakrabarti R (2006) A stable boundary element method for modeling transient acoustic radiation. J Acoust Soc Am 120(1):74–80.

Costabel M (2004) Time-dependent problems with the boundary integral equation method. Encycl Comput Mech 1:703–721.

Ergin A, Shanker B, Michielssen E (1999) Analysis of transient wave scattering from rigid bodies using a burton–miller approach. J Acoust Soc Am 106(5):2396–2404.

Ha-Duong T, Ludwig B, Terrasse I (2003) A Galerkin BEM for transient acoustic scattering by an absorbing obstacle. Int J Numer Methods Eng 57(13):1845–1882.

Hackbusch W, Kress W, Sauter SA (2008) Sparse convolution quadrature for time domain boundary integral formulations of the wave equation. IMA J Numer Anal 29(1):158–179.

Hu FQ, Pizzo ME, Nark DM (2017) On a time domain boundary integral equation formulation for acoustic scattering by rigid bodies in uniform mean flow. J Acoust Soc Am 142(6):3624–3636.

Lubich C (1994) On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations. Numer Math 67(3):365–389.

Lubich C (1988) Convolution quadrature and discretized operational calculus. I Numer Math 52(2):129–145.

Ergin A, Shanker B, Michielssen E (2000) Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm. J Acoust Soc Am 107(3):1168–1178.

Hu FQ (2013) An efficient solution of time domain boundary integral equations for acoustic scattering and its acceleration by graphics processing units In: 19th AIAA/CEAS Aeroacoustics Conference. AIAA paper 2013-2018.

Meng J, Boag A, Lomakin V, Michielssen E (2010) A multilevel cartesian non-uniform grid time domain algorithm. J Comput Phys 229(22):8430–8444.

Thirard C, Parot JM (2017) On a way to save memory when solving time domain boundary integral equations for acoustic and vibroacoustic applications. J Comput Phys 348:744–753.

Weile DS, Pisharody G, Chen NW, Shanker B, Michielssen E (2004) A novel scheme for the solution of the time-domain integral equations of electromagnetics. IEEE Trans Antennas Propag 52(1):283–295.

vant Wout E, van der Heul DR, van der Ven H, Vuik C (2013) Design of temporal basis functions for time domain integral equation methods with predefined accuracy and smoothness. IEEE Trans Antennas Propag 61(1):271–280.

Wang X, Weile DS (2011) Implicit Runge-Kutta methods for the discretization of time domain integral equations. IEEE Trans Antennas Propag 59(12):4651–4663.

Geranmayeh A, Ackermann W, Weiland T (2009) Temporal discretization choices for stable boundary element methods in electromagnetic scattering problems. Appl Numer Math 59(11):2751–2773.

vant Wout E, van der Heul DR, van der Ven H, Vuik C (2016) Stability analysis of the marching-on-in-time boundary element method for electromagnetics. J Comput Appl Math 294:358–371.

Strikwerda JC (2004) Finite difference schemes and partial differential equations, SIAM, Philadelphia, PA.

Dodson S, Walker S, Bluck M (1998) Implicitness and stability of time domain integral equation scattering analyses. Appl Comput Electromagn Soc J 13:291–301.