The Experts below are selected from a list of 106614 Experts worldwide ranked by ideXlab platform
Eero Vainikko - One of the best experts on this subject based on the ideXlab platform.
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domain decomposition preconditioning for high frequency helmholtz problems with absorption
IEEE Communications Magazine, 2017Co-Authors: Ivan G Graham, Euan A Spence, Eero VainikkoAbstract:In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation −∆u − (k2 + ie)u = f , with absorption parameter e ∈ R. Multigrid approximations of this equation with e 6= 0 are commonly used as preconditioners for the pure Helmholtz case (e = 0). However a rigorous theory for such (so-called “shifted Laplace”) preconditioners, either for the pure Helmholtz equation or even the damped equation, is still missing. We present a new theory for the damped equation that provides rates of convergence for (leftor right-) preconditioned GMRES, via estimates of the norm and field of values of the preconditioned matrix. This theory uses a kand e-explicit coercivity result for the underlying sesquilinear form and shows, for example, that if |e| ∼ k2, then classical overlapping additive Schwarz will perform optimally for the damped problem, provided the coarse mesh diameter is carefully chosen. Extensive numerical experiments illustrate the theory and also give insight into how domain decomposition approximations of the damped problem perform as preconditioners for the pure Helmholtz case. While the theory applies to a certain weighted variant of GMRES, the experiments for both weighted and classical GMRES give comparable results. At the end of the paper we propose a (scalable) multilevel preconditioner for the pure Helmholtz problem that has an empirical complexity of about O(n4/3) for solving finite element systems of size n = O(k3), where we have chosen the mesh diameter h ∼ k−3/2 to avoid the Pollution Effect. Experiments on problems with h ∼ k−1, i.e. a fixed number of grid points per wavelength, are also given.
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domain decomposition preconditioning for high frequency helmholtz problems with absorption
arXiv: Numerical Analysis, 2015Co-Authors: Ivan G Graham, Euan A Spence, Eero VainikkoAbstract:In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption parameter $\varepsilon \in \mathbb{R}$. Multigrid approximations of this equation with $\varepsilon \not= 0$ are commonly used as preconditioners for the pure Helmholtz case ($\varepsilon = 0$). However a rigorous theory for such (so-called "shifted Laplace") preconditioners, either for the pure Helmholtz equation, or even the absorptive equation ($\varepsilon \not=0$), is still missing. We present a new theory for the absorptive equation that provides rates of convergence for (left- or right-) preconditioned GMRES, via estimates of the norm and field of values of the preconditioned matrix. This theory uses a $k$- and $\varepsilon$-explicit coercivity result for the underlying sesquilinear form and shows, for example, that if $|\varepsilon|\sim k^2$, then classical overlapping additive Schwarz will perform optimally for the absorptive problem, provided the subdomain and coarse mesh diameters are carefully chosen. Extensive numerical experiments are given that support the theoretical results. The theory for the absorptive case gives insight into how its domain decomposition approximations perform as preconditioners for the pure Helmholtz case $\varepsilon = 0$. At the end of the paper we propose a (scalable) multilevel preconditioner for the pure Helmholtz problem that has an empirical computation time complexity of about $\mathcal{O}(n^{4/3})$ for solving finite element systems of size $n=\mathcal{O}(k^3)$, where we have chosen the mesh diameter $h \sim k^{-3/2}$ to avoid the Pollution Effect. Experiments on problems with $h\sim k^{-1}$, i.e. a fixed number of grid points per wavelength, are also given.
Ivan G Graham - One of the best experts on this subject based on the ideXlab platform.
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domain decomposition preconditioning for high frequency helmholtz problems with absorption
IEEE Communications Magazine, 2017Co-Authors: Ivan G Graham, Euan A Spence, Eero VainikkoAbstract:In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation −∆u − (k2 + ie)u = f , with absorption parameter e ∈ R. Multigrid approximations of this equation with e 6= 0 are commonly used as preconditioners for the pure Helmholtz case (e = 0). However a rigorous theory for such (so-called “shifted Laplace”) preconditioners, either for the pure Helmholtz equation or even the damped equation, is still missing. We present a new theory for the damped equation that provides rates of convergence for (leftor right-) preconditioned GMRES, via estimates of the norm and field of values of the preconditioned matrix. This theory uses a kand e-explicit coercivity result for the underlying sesquilinear form and shows, for example, that if |e| ∼ k2, then classical overlapping additive Schwarz will perform optimally for the damped problem, provided the coarse mesh diameter is carefully chosen. Extensive numerical experiments illustrate the theory and also give insight into how domain decomposition approximations of the damped problem perform as preconditioners for the pure Helmholtz case. While the theory applies to a certain weighted variant of GMRES, the experiments for both weighted and classical GMRES give comparable results. At the end of the paper we propose a (scalable) multilevel preconditioner for the pure Helmholtz problem that has an empirical complexity of about O(n4/3) for solving finite element systems of size n = O(k3), where we have chosen the mesh diameter h ∼ k−3/2 to avoid the Pollution Effect. Experiments on problems with h ∼ k−1, i.e. a fixed number of grid points per wavelength, are also given.
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domain decomposition preconditioning for high frequency helmholtz problems with absorption
arXiv: Numerical Analysis, 2015Co-Authors: Ivan G Graham, Euan A Spence, Eero VainikkoAbstract:In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption parameter $\varepsilon \in \mathbb{R}$. Multigrid approximations of this equation with $\varepsilon \not= 0$ are commonly used as preconditioners for the pure Helmholtz case ($\varepsilon = 0$). However a rigorous theory for such (so-called "shifted Laplace") preconditioners, either for the pure Helmholtz equation, or even the absorptive equation ($\varepsilon \not=0$), is still missing. We present a new theory for the absorptive equation that provides rates of convergence for (left- or right-) preconditioned GMRES, via estimates of the norm and field of values of the preconditioned matrix. This theory uses a $k$- and $\varepsilon$-explicit coercivity result for the underlying sesquilinear form and shows, for example, that if $|\varepsilon|\sim k^2$, then classical overlapping additive Schwarz will perform optimally for the absorptive problem, provided the subdomain and coarse mesh diameters are carefully chosen. Extensive numerical experiments are given that support the theoretical results. The theory for the absorptive case gives insight into how its domain decomposition approximations perform as preconditioners for the pure Helmholtz case $\varepsilon = 0$. At the end of the paper we propose a (scalable) multilevel preconditioner for the pure Helmholtz problem that has an empirical computation time complexity of about $\mathcal{O}(n^{4/3})$ for solving finite element systems of size $n=\mathcal{O}(k^3)$, where we have chosen the mesh diameter $h \sim k^{-3/2}$ to avoid the Pollution Effect. Experiments on problems with $h\sim k^{-1}$, i.e. a fixed number of grid points per wavelength, are also given.
Michelle Wilhelm - One of the best experts on this subject based on the ideXlab platform.
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ambient air Pollution and adverse birth outcomes methodologic issues in an emerging field
Basic & Clinical Pharmacology & Toxicology, 2008Co-Authors: Beate Ritz, Michelle WilhelmAbstract:Since the mid-1990s, the number of studies linking air pollutants to low birthweight, small for gestational age, preterm birth and cardiac birth defects has grown steadily. This MiniReview (in conjunction with the May 2007 International Conference on Foetal Programming and Development Toxicity) highlights key methodological issues surrounding this research area, based on our experiences in Southern California. All 'criteria' air pollutants have been linked to birth outcomes. Our own studies found most consistent associations for carbon monoxide and particles. Traffic exhaust toxins are possible causative agents, but air monitoring data relied on by almost all existing studies inadequately capture their intracommunity variability in concentrations. Exposure assessment might be improved by biomarkers and land use-based regression modelling or information on time-activity patterns. Foetal development provides unique opportunities to study exposures acting during narrow susceptibility windows. A time-series approach by design controls for confounders that do not vary temporally but can only address short-term acute Effects. Studies employing spatial or medium-term (trimester-specific) temporal contrasts may be more susceptible to residual confounding, and studies adjusting only for risk factors recorded on birth certificates have been criticized. Findings from our recent study in Southern California indicate that air Pollution Effect estimates are not markedly influenced by risk factors not provided on birth certificates. Yet, studies collecting detailed risk factor information in other geographic regions may be needed to further evaluate the extent of residual confounding in record-based analyses. Investigating biological mechanisms (e.g. using ultrasound measurements and biomarkers for hypothesized pathways) is an important remaining issue.
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ambient air Pollution and preterm birth in the environment and pregnancy outcomes study at the university of california los angeles
American Journal of Epidemiology, 2007Co-Authors: Beate Ritz, Michelle Wilhelm, Katherine J Hoggatt, Jo Kay GhoshAbstract:The authors conducted a case-control survey nested within a birth cohort and collected detailed risk factor information to assess the extent to which residual confounding and exposure misclassification may impact air Pollution Effect estimates. Using a survey of 2,543 of 6,374 women sampled from a cohort of 58,316 eligible births in 2003 in Los Angeles County, California, the authors estimated with logistic regression and two-phase models the Effects of pregnancy period-specific air Pollution exposure on the odds of preterm birth. For the first trimester, the odds of preterm birth consistently increased with increasing carbon monoxide exposures and also at high levels of exposure to particulate matter less than or equal to 2.5 μm in diameter (>21.4 μg/m 3 ), regardless of type of data (cohort/sample) or covariate adjustment (carbon monoxide exposures of >1.25 ppm increased the odds by 21-25%). Women exposed to carbon monoxide above 0.91 ppm during the last 6 weeks of pregnancy experienced increased odds of preterm birth. Crude and birth certificate covariate-adjusted results for carbon monoxide differed from each other. However, further adjustment for risk factors assessed in the survey did not change Effect estimates for short-term pollutant averages appreciably, except for time-activity patterns, which strengthened the observed associations. These results confirm the importance of reducing exposure misclassification when evaluating the Effect of traffic-related pollutants that vary spatially.
Victor M Calo - One of the best experts on this subject based on the ideXlab platform.
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a class of discontinuous petrov galerkin methods part iv the optimal test norm and time harmonic wave propagation in 1d
Journal of Computational Physics, 2011Co-Authors: J Zitelli, Ignacio Muga, Leszek Demkowicz, Jay Gopalakrishnan, David Pardo, Victor M CaloAbstract:The phase error, or the Pollution Effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method is constructed within the framework of the discontinuous Petrov-Galerkin (DPG) method with optimal test functions. We have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test space norm. In this paper, we advance by asking what is the optimal test space norm that achieves error reduction in a given energy norm. This is answered in the specific case of the Helmholtz equation with L^2-norm as the energy norm. We obtain uniform stability with respect to the wave number. We illustrate the method with a number of 1D numerical experiments, using discontinuous piecewise polynomial hp spaces for the trial space and its corresponding optimal test functions computed approximately and locally. A 1D theoretical stability analysis is also developed.
Beate Ritz - One of the best experts on this subject based on the ideXlab platform.
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ambient air Pollution and adverse birth outcomes methodologic issues in an emerging field
Basic & Clinical Pharmacology & Toxicology, 2008Co-Authors: Beate Ritz, Michelle WilhelmAbstract:Since the mid-1990s, the number of studies linking air pollutants to low birthweight, small for gestational age, preterm birth and cardiac birth defects has grown steadily. This MiniReview (in conjunction with the May 2007 International Conference on Foetal Programming and Development Toxicity) highlights key methodological issues surrounding this research area, based on our experiences in Southern California. All 'criteria' air pollutants have been linked to birth outcomes. Our own studies found most consistent associations for carbon monoxide and particles. Traffic exhaust toxins are possible causative agents, but air monitoring data relied on by almost all existing studies inadequately capture their intracommunity variability in concentrations. Exposure assessment might be improved by biomarkers and land use-based regression modelling or information on time-activity patterns. Foetal development provides unique opportunities to study exposures acting during narrow susceptibility windows. A time-series approach by design controls for confounders that do not vary temporally but can only address short-term acute Effects. Studies employing spatial or medium-term (trimester-specific) temporal contrasts may be more susceptible to residual confounding, and studies adjusting only for risk factors recorded on birth certificates have been criticized. Findings from our recent study in Southern California indicate that air Pollution Effect estimates are not markedly influenced by risk factors not provided on birth certificates. Yet, studies collecting detailed risk factor information in other geographic regions may be needed to further evaluate the extent of residual confounding in record-based analyses. Investigating biological mechanisms (e.g. using ultrasound measurements and biomarkers for hypothesized pathways) is an important remaining issue.
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ambient air Pollution and preterm birth in the environment and pregnancy outcomes study at the university of california los angeles
American Journal of Epidemiology, 2007Co-Authors: Beate Ritz, Michelle Wilhelm, Katherine J Hoggatt, Jo Kay GhoshAbstract:The authors conducted a case-control survey nested within a birth cohort and collected detailed risk factor information to assess the extent to which residual confounding and exposure misclassification may impact air Pollution Effect estimates. Using a survey of 2,543 of 6,374 women sampled from a cohort of 58,316 eligible births in 2003 in Los Angeles County, California, the authors estimated with logistic regression and two-phase models the Effects of pregnancy period-specific air Pollution exposure on the odds of preterm birth. For the first trimester, the odds of preterm birth consistently increased with increasing carbon monoxide exposures and also at high levels of exposure to particulate matter less than or equal to 2.5 μm in diameter (>21.4 μg/m 3 ), regardless of type of data (cohort/sample) or covariate adjustment (carbon monoxide exposures of >1.25 ppm increased the odds by 21-25%). Women exposed to carbon monoxide above 0.91 ppm during the last 6 weeks of pregnancy experienced increased odds of preterm birth. Crude and birth certificate covariate-adjusted results for carbon monoxide differed from each other. However, further adjustment for risk factors assessed in the survey did not change Effect estimates for short-term pollutant averages appreciably, except for time-activity patterns, which strengthened the observed associations. These results confirm the importance of reducing exposure misclassification when evaluating the Effect of traffic-related pollutants that vary spatially.