The Helmholtz equation arises when modeling wave propagation in the frequency domain. The equation is discretized as an indefinite linear system, which is difficult to solve at high wave numbers. In many applications, the solution of the Helmholtz equation is required for a point source. In this case, it is possible to reformulate the equation as two separate equations: one for the travel time ...

In this paper we give analytical evidence of increasing stability in the Cauchy Problem for the Helmholtz equation when frequency is growing. This effect depends on convexity properties of the surface where the Cauchy Data are given and on some monotonicity properties of the variable coefficient of the Helmholtz equation. Proofs use Carleman estimates and the theory of elliptic and hyperbolic b...

We show how a number of second order time-dependent partial differential equations can be solved numerically by reformulating them in terms of inhomogeneous modified Helmholtz equations. Using recently derived analytic particular solutions for these equations, the resulting boundary value problems can be reduced to solving homogeneous Helmholtz equations which can be done effectively using the ...

R. Feyerherm, ∗ E. Dudzik, A. U. B. Wolter, 2, † S. Valencia, O. Prokhnenko, A. Maljuk, S. Landsgesell, N. Aliouane, ‡ L. Bouchenoire, S. Brown, and D. N. Argyriou Helmholtz-Zentrum Berlin, BESSY, 12489 Berlin, Germany Institut für Physik der Kondensierten Materie, Technical University Braunschweig, 38106 Braunschweig, Germany Helmholtz-Zentrum Berlin, 14109 Berlin, Germany XMaS CRG Beamline, E...

Drug Delivery (DDEL), Helmholtz-Institute for Pharmaceutical Research Saarland (HIPS), Saarbrücken, Germany; Department of Pharmacy, Saarland University, Saarbrücken, Germany; Department of Biosciences, University of Oslo, Oslo, Norway; Saarland University, Institute of Human Genetics, University Hospital, Homburg/Saar, Germany; SHG Clinics, Department of Cardiothoracic Surgery, Voelklingen Hea...

In this talk I will discuss a method to prove the absence of critical points for the Helmholtz equation in 3D. The key element of the approach is the use of multiple frequencies in a fixed range, and the proof is based on the spectral analysis of the associated problem. This question is strictly connected with the Radó-Kneser-Choquet theorem, whose direct extension to the Helmholtz equation or ...

3 Ernest Marco-Urrea, Jana Seifert, Martin von Bergen, Lorenz Adrian 4 5 1 Helmholtz Centre for Environmental Research UFZ, Department Isotope 6 Biogeochemistry, Permoserstraβe 15, 04318 Leipzig, Germany. 7 2 Department of Chemical Engineering, Autonomous University of Barcelona, 08193 8 Cerdanyola del Vallés, Spain. 9 3 Helmholtz Centre for Environmental Research UFZ, Department of Proteomics,...

The Finite Element Tearing and Interconnecting method for the Helmholtz equation is a recent non-overlapping domain decomposition method for solving linear systems arising from the nite element discretization of Helmholtz problems in bounded domains. This method was validated on two-dimensional external problems with rst order absorbing boundary conditions. The purpose of this paper is to study...

Heiko Zimmermann ([email protected]) Daniel Hagenfeld ([email protected]) Katja Diercke ([email protected]) Nihad El-Sayed ([email protected]) Julia Fricke ([email protected]) Karin Halina Greiser ([email protected]) Jan Kühnisch ([email protected]) Jakob Linseisen ([email protected]) C...

It is shown by counterexamples that Green's functions describing the propagation of a field from one surface to another do not, in general, satisfy Helmholtz's reciprocity theorem. Inhalt Zur Ungültigkeit des Reziprozitätstheorems von Helmholtz für Greensehe Funk-tionen zur Beschreibung der Fortpflanzung eines sakalaren Wellenfeldes in nicht-leerem und leerem Raum. Wie durch Gegenbeispiele geze...