Martin Schanz is Professor of Mechanics at the Department of Civil Engineering at Graz University of Technology. He studied mechanical engineering at the University of Karlsruhe (Germany) and earned his Diploma degree in 1990. From 1990 he investigated in improving the BEM formulation for wave propagation problems. His doctoral thesis is about viscoelastic BEM formulations in time domain. He received his habilitation in Mechanics in 2001 with a thesis on a visco- and poroelastodynamic BEM formulation. He had  research stays at the University of Delaware (USA), the University of Campinas (Brazil), the Hong Kong University of Science and Technology (China) and the University of Zurich (Switzerland). He has authored and co-authored more then 50 journal papers, four books, and several book chapters. His research interests cover visco- and poroelasticity and the acoustic behavior of such materials. The main focus lies on the development of Boundary Element Methods with focus on wave propagation, which includes also fast methods like FMM and ACA. He is actually president of the International Association for Boundary Element Methods (IABEM) and associate editor of Applied Mechanics Reviews beside other services at  Graz University of Technology.

Variable Time Steps in Time Domain Boundary Elements

Martin Schanz
Institute of Applied Mechanics
Graz University of Technology
Technikerstr. 4 / 2nd floor
A-8010 Graz

E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.


In acoustics often infinite or semi-infinte domains has to be treated, e.g., scattering.  As long as travelling waves are considered a time domain calculation is advantageous.  A preferable method to simulate the waves in such domains is the Boundary Element Method in time domain. The radiation
condition is fulfilled in this method,  but the numerical effort is high.   Especially in time domain, efficient methods are challenging.  The quadratic complexity in the spatial variable may be reduced by so-called fast methods.  However, to keep the linear complexity in time a constant time step size is required, which is not a suitable choice for all problems.  If a non-smooth time behavior has to be captured a variable step size would be the better choice.
    A variable time step size for BEM has been proposed by Sauter and Veit [3] using a global shape function in time and by Lopez-Fernandez and Sauter [1, 2] with a generalized convolution quadrature method (gCQM). Both approaches are formulated for the single layer potential in acoustics. The
gCQM approach shares all benefits of the original convolution quadrature method but allows a variable time step size. The complexity in time is O (N log N). This approach is used in this presentation to establish BE formulations for an acoustic domain with absorbing boundary conditions. Numerical studies will show the behaviour of this formulation with respect to temporal discretization. The sound pressure in a building will serve as real world application [4].

[1]  M. Lopez-Fernandez and S. Sauter, Generalized convolution quadrature with variable time stepping, IMA J. of Numer. Anal. 33 (2013), no. 4, 1156–1175.
[2]  ____,Generalized convolution quadrature with variable time stepping. part II: Algorithm and numerical results, Appl. Num. Math. 94 (2015), 88–105.
[3]  S. Sauter and A. Veit, A Galerkin method for retarded boundary integral equations with smooth and compactly supported temporal basis functions, Numer. Math.123 (2013), no. 1, 145–176.
[4]  S.A.  Sauter  and  M.  Schanz, Convolution quadrature for the wave equation with impedance boundary conditions, J. Comput. Phys. 334 (2017), 442–459.


JSN Epic template designed by