A calderón multiplicative preconditioner for the combined field integral equation
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Computational Electromagnetics Laboratory
Permanent link to this recordhttp://hdl.handle.net/10754/561446
MetadataShow full item record
AbstractA Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation is resonance-free. The iterative solution of the linear system of equations obtained via the CMP-based discretization of the CFIE converges rapidly regardless of the discretization density and the frequency of excitation. © 2009 IEEE.
SponsorsManuscript received October 17, 2008; revised January 27, 2009. First published August 07, 2009; current version published October 07, 2009. This work was supported in part by AFOSR MURI Grant F014432-051936, aimed at modeling installed antennas and their feeds, and by NSF Grant DMS 0713771.
Showing items related by title, author, creator and subject.
Integration of two-phase solid fluid equations in a catchment model for flashfloods, debris flows and shallow slope failuresBout, B.; Lombardo, Luigi; van Westen, C.J.; Jetten, V.G. (Environmental Modelling & Software, Elsevier BV, 2018-04-09) [Article]An integrated, modeling method for shallow landslides, debris flows and catchment hydrology is developed and presented in this paper. Existing two-phase debris flow equations and an adaptation on the infinite slope method are coupled with a full hydrological catchment model. We test the approach on the 4 km2 Scaletta catchment, North-Eastern Sicily, where the 1-10-2009 convective storm caused debris flooding after 395 shallow landslides. Validation is done based on the landslide inventory and photographic evidence from the days after the event. Results show that the model can recreate the impact of both shallow landslides, debris flow runout, and debris floods with acceptable accuracy (91 percent inventory overlap with a 0.22 Cohens Kappa). General patterns in slope failure and runout are well-predicted, leading to a fully physically based prediction of rainfall induced debris flood behavior in the downstream areas, such as the creation of a debris fan at the coastal outlet.
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemesAuzinger, Winfried; Hofstätter, Harald; Ketcheson, David I.; Koch, Othmar (BIT Numerical Mathematics, Springer Nature, 2016-07-28) [Article]We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial systems for the splitting coefficients. To this end we use and modify a recent approach for generating these systems for a large class of splittings. In particular, various types of pairs of schemes intended for use in adaptive integrators are constructed.
Transient Electromagnetic Analysis of Complex Penetrable Scatterers using Volume Integral EquationsSayed, Sadeed B (2018-11) [Dissertation]
Advisor: Bagci, Hakan
Committee members: Bagci, Hakan; Ooi, Boon S.; Samtaney, Ravi; Andriulli, Francesco P.Simulation tools capable of analyzing electromagnetic (EM) field/wave interactions on complex penetrable scatterers have applications in various areas of engineering ranging from the design of integrated antennas to the subsurface imaging. EM simulation tools operating in the time domain can be formulated to directly solve the Maxwell equations or the integral equations obtained by enforcing fundamental field relations or boundary conditions. Time domain integral equation (TDIE) solvers offer several benefits over differential equation solvers: They require smaller number discretization elements/sampling points (both in space and time). Despite the advantages, TDIE solvers suffer from increased computational cost, stability issues of the time-marching algorithms, and limited applicability to complex scatterers. This thesis is focused on addressing the last two issues associated with time domain volume integral equation (TD-VIE) solvers, as the issue of increased computational cost has been addressed by recently developed acceleration methods. More specifically, four new closely-related, but different marching on-in-time (MOT) algorithms are formulated and implemented to solve the time domain electric and magnetic field volume integral equations (TD-EFVIE and TD-MFVIE). The first algorithm solves the TD-EFVIE to analyze EM wave interactions on high-contrast dielectric scatterers. The stability of this MOT scheme is ensured by using two-sided approximate prolate spherical wave (APSW) functions to discretize the time dependence of the unknown current density as well as an extrapolation scheme to restore the causality of matrix system resulting from this discretization. The second MOT scheme solves the TDMFVIE to analyze EM wave interactions on dielectric scatterers. The TD-MFVIE is cast in the form of an ordinary differential equation (ODE) and the unknown magnetic field is expanded using spatial basis functions. The time-dependent coefficients of this expansion are found by integrating the resulting ODE system using a linear multistep method. The third method is formulated and implemented to analyze EM wave interactions on scatterers with Kerr nonlinearity. The former scheme integrates in time a coupled of system of the TD-EFVIE and the nonlinear constitutive relation, which is cast in the form of an ODE system, for the expansion coefficients of the electric field and flux using a linear multistep method. The last method described in this thesis is developed to analyze EM wave interactions on ferrite scatterers.