Automatically Adapted Perfectly Matched Layers for Problems with High Contrast Materials Properties

AbstractFor the simulation of wave propagation problems, it is necessary to truncate the computational domain. Perfectly Matched Layers are often employed for that purpose, especially in high contrast layered materials where absorbing boundary conditions are difficult to design. In here, we define a Perfectly Matched Layer that automatically adjusts its parameters without any user interaction. The user only has to indicate the desired decay in the surrounding layer. With this Perfectly Matched Layer, we show that even in the most complex scenarios where the material contrast properties are as high as sixteen orders of magnitude, we do not introduce numerical reflections when truncating the domain, thus, obtaining accurate solutions

High-frequency analysis of the efficiency of a local approximate DtN2 boundary condition for prolate spheroidal-shaped boundaries

The performance of the second-order local approximate DtN boundary condition suggested in [4] is investigated analytically when employed for solving high-frequency exterior Helmholtz problems with elongated scatterers. This study is performed using a domain-based formulation and assuming the scatterer and the exterior artificial boundary to be prolate spheroid. The analysis proves that, in the high-frequency regime, the reflected waves at the artificial boundary decay faster than 1/(ka)15/8, where k is the wavenumber and a is the semi-major axis of this boundary. Numerical results are presented to illustrate the accuracy and the efficiency of the proposed absorbing boundary condition, and to provide guidelines for satisfactory performance

Exponential decay of high-order spurious prolate spheroidal modes induced by a local approximate dtn exterior boundary condition

We investigate analytically the asymptotic behavior of high-order spurious prolate spheroidal modes induced by a second-order local approximate DtN absorbing boundary condition (DtN2) when employed for solving high-frequency acoustic scattering problems. We prove that these reflected modes decay exponentially in the high frequency regime. This theoretical result demonstrates the great potential of the considered absorbing boundary condition for solving efficiently exterior high-frequency Helmholtz problems. In addition, this exponential decay proves the superiority of DtN2 over the widely used Bayliss-Gunsburger-Turkel absorbing boundary condition

Quantities of interest for surface based resistivity geophysical measurements

The objective of traditional goal-oriented strategies is to construct an optimal mesh that minimizes the problem size needed to achieve a user prescribed tolerance error for a given quantity of interest (QoI). Typical geophysical resistivity measurement acquisition systems can easily record electromagnetic (EM) fields. However, depending upon the application, EM fields are sometimes loosely related to the quantity that is to be inverted (conductivity or resistivity), and therefore they become inadequate for inversion. In the present work, we study the impact of the selection of the QoI in our inverse problem. We focus on two different acquisition systems: marine controlled source electromagnetic (CSEM), and magnetotellurics (MT). For both applications, numerical results illustrate the benefits of employing adequate QoI. Specifically, the use as QoI of the impedance matrix on MT measurements provides significant computational savings, since one can replace the existing absorbing boundary conditions (BCs) by a homogeneous Dirichlet BC to truncate the computational domain, something that is not possible when considering EM fields as QoI

Non-reflecting boundary condition on ellipsoidal boundary

The modeling of wave propagation problems using finite element methods usually requires the truncation of the computation domain around the scatterer of interest. Absorbing boundary conditions are classically considered in order to avoid spurious reflections. In this paper, we investigate some properties of the Dirichlet to Neumann map posed on a spheroidal boundary in the context of the Helmholtz equation

Gastrointestinal symptoms and association with medication use patterns, adherence, treatment satisfaction, quality of life, and resource use in osteoporosis: baseline results of the MUSIC-OS study

Summary: The Medication Use Patterns, Treatment Satisfaction, and Inadequate Control of Osteoporosis Study (MUSIC-OS) is a prospective, observational study of women with osteoporosis in Europe and Canada. At baseline, patients with gastrointestinal symptoms reported lower adherence to osteoporosis treatment, treatment satisfaction, and health-related quality of life, than those without gastrointestinal symptoms. Introduction: The aim of the study was to examine gastrointestinal (GI) symptoms and the association between GI symptoms and treatment adherence, treatment satisfaction, and health-related quality of life (HRQoL) among osteoporotic women in Europe and Canada. Methods: Baseline results are reported here for a prospective study which enrolled postmenopausal, osteoporotic women who were initiating (new users) or continuing (experienced users) osteoporosis treatment at study entry (baseline). A patient survey was administered at baseline and included the occurrence of GI symptoms during 6-month pre-enrolment, treatment adherence (adherence evaluation of osteoporosis (ADEOS), score 0–22), treatment satisfaction (Osteoporosis Treatment Satisfaction Questionnaire for Medications (OPSAT-Q), score 0–100) and HRQoL (EuroQol-5 dimension (EQ-5D) utility, score 0–1; OPAQ-SV, score 0–100). The association between GI symptoms and ADEOS (experienced users), OPSAT-Q (experienced users), and HRQoL (new and experienced users) was assessed by general linear models adjusted for patient characteristics. Results: A total of 2959 patients (2275 experienced and 684 new users) were included. Overall, 68.1 % of patients experienced GI symptoms in the past 6 months. Compared with patients without GI symptoms, patients with GI symptoms had lower mean baseline scores on most measures. The mean adjusted differences were ADEOS, −0.43; OPSAT-Q, −5.68; EQ-5D, −0.04 (new users) and −0.06 (experienced users), all P < 0.01. GI symptoms were also associated with lower OPAQ-SV domain scores: physical function, −4.17 (experienced users); emotional status, −4.28 (new users) and −5.68 (experienced users); back pain, −5.82 (new users) and −11.33 (experienced users), all P < 0.01. Conclusions: Patients with GI symptoms have lower treatment adherence and treatment satisfaction and worse HRQoL than patients without GI symptoms

Approximate boundary conditions based on a complete transparent condition for the acoustic wave equation

National audienceThe numerical simulation of scattering problems generally involves particular boundary conditions set on the exterior boundary of the computational domain. These conditions are called Absorbing Boundary Conditions (ABC) when they satisfy the following properties; ABCs correspond to the approximation of a transparent condition, involve differential operators and minimize the reflections generated by the exterior boundary. Despite the works carried out on the design of ABCs, the existing ABCs need to be optimized and, recently, a new ABC has been proposed by Hagstrom et al. . It is an improved Higdon ABC (IHABC) where the amplitude of reflected waves is minimized by including a differential operator into the condition to model evanescent waves. The IHABC is very efficient when coupled with a finite element method, but it seems to hamper the Courant-Friedrichs-Lewy (CFL) condition when included into a Discontinuous Galerkin Method (DGM). Moreover, this condition is not easy to apply on arbitrarily-shaped boundaries. In this work, we address the issue of designing optimized ABCs which do not penalize the CFL condition when applying a DGM. We consider optimized ABCs adapted to arbitrarily-shaped regular boundaries and we construct a transparent condition based on the decomposition of the exact solution into a propagating field, an evanescent field and a grazing field. Then, a new condition is obtained by combining the approximations of the transparent condition in the three corresponding regions. It is not classical since it involves a fractional derivative arising from the grazing part of the solution. However, the condition is easily included into a finite element scheme and we have implemented it into an Interior Penalty Discontinuous Galerkin formulation. Numerical experiments have been performed and the results have shown that it does not modify the CFL condition. Furthermore, the absorption rate is improved when compared to classical ABCs