Journal of Water Supply: Research and Technology-Aqua, 2015
ABSTRACT This paper presents a methodology to assess and reduce water residence times in a water ... more ABSTRACT This paper presents a methodology to assess and reduce water residence times in a water distribution system in order to improve water quality. The methodology was developed and validated on Quebec City's main distribution system. A tracer study was conducted to evaluate real residence times and results are presented in the 'companion paper' (Part I) in this issue. A hydraulic model was then built to simulate the mean residence times (MRT) and develop strategies to reduce them. An optimization algorithm (hybrid discrete dynamically dimensioned search, HD-DDS) was used to calibrate the model using flows and pressures measured in the distribution system. Results show that the suggested methodology can lead to significant reductions in MRT (25.6%) in parts of the distribution system, but could also lead to significant loss in pressure, which should be monitored closely.
We derive error estimates for a fully discrete scheme for the numerical solution of the neutron t... more We derive error estimates for a fully discrete scheme for the numerical solution of the neutron transport equation in two-dimensional Cartesian geometry obtained by using a special quadrature rule for the angular variable and the discontinuous Galerkin finite element method with piecewise linear trial function for the space variable.
One way of improving the behavior of finite element schemes for classical, timedependent Maxwell’... more One way of improving the behavior of finite element schemes for classical, timedependent Maxwell’s equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear finite element method for the time harmonic Maxwell’s equations in a dual form obtained through the Laplace transformation in time. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. For the stabilized model a coercivity relation is derived that guarantee’s the existence of a unique solution for the discrete problem. The convergence is addressed both in a priori and a posteriori settings. In the a priori error estimates we confirm the theoretical convergence of the scheme in a L2-based, gradient dependent, triple norm. The order of convergence is O(h) in weighted Sobolev space H2 w(Ω), and hence optimal. Here, w = w(ε, s) where ε is the dielectric permittiv...
In this paper we deal with construction and analysis of a multiwavelet spectral element scheme fo... more In this paper we deal with construction and analysis of a multiwavelet spectral element scheme for a generalized Cauchy type problem with Caputo fractional derivative. Numerical schemes for this type of problems, often suffer from the draw-back of spurious oscillations. A common remedy is to render the problem to an equivalent integral equation. For the generalized Cauchy type problem, a corresponding integral equation is of nonlinear Volterra type. In this paper we investigate wellposedness and convergence of a stabilizing multiwavelet scheme for a, one-dimensional case (in [a, b] or [0, 1]), of this problem. Based on multiwavelets, we construct an approximation procedure for the fractional integral operator that yields a linear system of equations with sparse coefficient matrix. In this setting, choosing an appropriate threshold, the number of non-zero coefficients in the system is substantially reduced. A severe obstacle in the convergence analysis is the lack of continuous deriv...
TJ ARBOGAST (University of Texas at Austin, USA) R. ALAM (IIT Guwahati, India) S. AL-HOMIDAN (Uni... more TJ ARBOGAST (University of Texas at Austin, USA) R. ALAM (IIT Guwahati, India) S. AL-HOMIDAN (University of Waterloo, Canada) M. ASADZADEH (Chalmers Institute of Technology, Sweden) M. BARTHOLOMEW-BIGGS (University of Hertfordshire, UK) RK BEATSON (University of Canterbury, New Zealand) R. BECKER (Universität Heidelberg, Germany) FB BELGACEM (Université Paul Sabatier, France) S. BERRES (Universität Stuttgart, Germany) ˚A. BJ ¨ORCK (University of Linköping, Sweden) L. BLANK (Universität Regensburg, Germany) JF ...
We study a combined variational (finite element) and quadrature approximation for some semilinear... more We study a combined variational (finite element) and quadrature approximation for some semilinear parabolic problems and give semidiscrete (space discretization) error analysis based on nonlinear semigroup techniques and Sobolev imbeddings. Optimal convergence rates are given for both smooth and nonsmooth data and with solution and gradient depending nonlinearities.
Mathematical Models and Methods in Applied Sciences, 1992
We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arisin... more We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.
Mathematical Models and Methods in Applied Sciences, 2007
We analyze the hp-version of the streamline diffusion finite element method for the Vlasov–Fokker... more We analyze the hp-version of the streamline diffusion finite element method for the Vlasov–Fokker–Planck system. For this method we prove the stability estimates and derive sharp a priori error bounds in a stabilization parameter δ ~ min (h/p, h2/σ), with h denoting the mesh size of the finite element discretization in phase-space-time, p the spectral order of approximation, and σ the transport cross-section.
Computer Methods in Applied Mechanics and Engineering, 2002
We consider a Fermi pencil-beam model in two-space dimensions ðx; yÞ, where x is aligned with the... more We consider a Fermi pencil-beam model in two-space dimensions ðx; yÞ, where x is aligned with the beam's penetration direction and y together with the scaled angular variable z correspond to a, bounded symmetric, transversal cross-section. The model corresponds to a forward-backward degenerate, convection dominated, convection-diffusion problem. For this problem we study some fully discrete numerical schemes using the standard-and Petrov-Galerkin finite element methods, for discretizations of the transversal domain, combined with the backward Euler, Crank-Nicolson, and discontinuous Galerkin methods for discretizations in the penetration variable. We derive stability estimates for the semi-discrete problems. Further, assuming sufficiently smooth exact solution, we obtain optimal a priori error bounds in a triple norm. These estimates give rise to a priori error estimates in the L 2-norm. Numerical implementations presented for some examples with the data approximating Dirac d function, confirm the expected performance of the combined schemes.
and discrete ordinates approximations for neutron transport equation and the critical eigenvalue ... more and discrete ordinates approximations for neutron transport equation and the critical eigenvalue M. ASADZADEH
Abstract. We give a survey of computational algorithms derived in a series of papers for solution... more Abstract. We give a survey of computational algorithms derived in a series of papers for solution of a synthesis problem for optimal stabilization of periodic systems. The proposed algorithms synthesize reliable control, with a given stability tolerance, for periodic systems optimized with respect to the quadratic performance criterion. A reliable controller guarantees the stability and is nearly a linear/quadratic regulator. We also consider the inverse problems for optimal synthesis corresponding to quadratic functionals. The algorithms designed to solve this problem are based on methods of linear matrix inequalities. The efficiency of the proposed algorithms are shown through implementing some examples. In this note we give an overview of computational algorithms for solution of a synthesis problem for optimal stabilization of periodic systems. Our study is based on stability of a discrete algebraic Riccati equation (ARE). The main feature of this study is to define an optimal re...
The paper considers the convergence study of the stabilized P1 finite element method for the time... more The paper considers the convergence study of the stabilized P1 finite element method for the time harmonic Maxwell’s equations. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. For the stabilized model a coercivity relation is derived that guarantee’s the existence of a unique solution for the discrete problem. The convergence is addressed both in a priori and a posteriori settings. Our numerical examples validate obtained convergence results.
This note is a study of combined Daubechies (Db2) wavelet transform and the statistical parameter... more This note is a study of combined Daubechies (Db2) wavelet transform and the statistical parameters skewness and kurtosis applied to detection of microcalcification in mammography. We have succintly introduced the concept of vanishing moments and derived scaling and wavelet functions using generating functions. The efficiency of the discrete algorithm is heavily relied on the order of performing wavelet approximation and the statistical procedure. The vital importance of both wavelet and statistical parameter approaches as well as the ordering issue in performing the analysis are justified through implementing numerical examples for some clinical data.
Abstract. This paper presents a nonstandard local approach to Richardson extrapolation, when it i... more Abstract. This paper presents a nonstandard local approach to Richardson extrapolation, when it is used to increase the accuracyof the standard finite element approximation of solutions of second order elliptic boundaryvalue problems in ℝ
Journal of Water Supply: Research and Technology-Aqua, 2015
ABSTRACT This paper presents a methodology to assess and reduce water residence times in a water ... more ABSTRACT This paper presents a methodology to assess and reduce water residence times in a water distribution system in order to improve water quality. The methodology was developed and validated on Quebec City's main distribution system. A tracer study was conducted to evaluate real residence times and results are presented in the 'companion paper' (Part I) in this issue. A hydraulic model was then built to simulate the mean residence times (MRT) and develop strategies to reduce them. An optimization algorithm (hybrid discrete dynamically dimensioned search, HD-DDS) was used to calibrate the model using flows and pressures measured in the distribution system. Results show that the suggested methodology can lead to significant reductions in MRT (25.6%) in parts of the distribution system, but could also lead to significant loss in pressure, which should be monitored closely.
We derive error estimates for a fully discrete scheme for the numerical solution of the neutron t... more We derive error estimates for a fully discrete scheme for the numerical solution of the neutron transport equation in two-dimensional Cartesian geometry obtained by using a special quadrature rule for the angular variable and the discontinuous Galerkin finite element method with piecewise linear trial function for the space variable.
One way of improving the behavior of finite element schemes for classical, timedependent Maxwell’... more One way of improving the behavior of finite element schemes for classical, timedependent Maxwell’s equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear finite element method for the time harmonic Maxwell’s equations in a dual form obtained through the Laplace transformation in time. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. For the stabilized model a coercivity relation is derived that guarantee’s the existence of a unique solution for the discrete problem. The convergence is addressed both in a priori and a posteriori settings. In the a priori error estimates we confirm the theoretical convergence of the scheme in a L2-based, gradient dependent, triple norm. The order of convergence is O(h) in weighted Sobolev space H2 w(Ω), and hence optimal. Here, w = w(ε, s) where ε is the dielectric permittiv...
In this paper we deal with construction and analysis of a multiwavelet spectral element scheme fo... more In this paper we deal with construction and analysis of a multiwavelet spectral element scheme for a generalized Cauchy type problem with Caputo fractional derivative. Numerical schemes for this type of problems, often suffer from the draw-back of spurious oscillations. A common remedy is to render the problem to an equivalent integral equation. For the generalized Cauchy type problem, a corresponding integral equation is of nonlinear Volterra type. In this paper we investigate wellposedness and convergence of a stabilizing multiwavelet scheme for a, one-dimensional case (in [a, b] or [0, 1]), of this problem. Based on multiwavelets, we construct an approximation procedure for the fractional integral operator that yields a linear system of equations with sparse coefficient matrix. In this setting, choosing an appropriate threshold, the number of non-zero coefficients in the system is substantially reduced. A severe obstacle in the convergence analysis is the lack of continuous deriv...
TJ ARBOGAST (University of Texas at Austin, USA) R. ALAM (IIT Guwahati, India) S. AL-HOMIDAN (Uni... more TJ ARBOGAST (University of Texas at Austin, USA) R. ALAM (IIT Guwahati, India) S. AL-HOMIDAN (University of Waterloo, Canada) M. ASADZADEH (Chalmers Institute of Technology, Sweden) M. BARTHOLOMEW-BIGGS (University of Hertfordshire, UK) RK BEATSON (University of Canterbury, New Zealand) R. BECKER (Universität Heidelberg, Germany) FB BELGACEM (Université Paul Sabatier, France) S. BERRES (Universität Stuttgart, Germany) ˚A. BJ ¨ORCK (University of Linköping, Sweden) L. BLANK (Universität Regensburg, Germany) JF ...
We study a combined variational (finite element) and quadrature approximation for some semilinear... more We study a combined variational (finite element) and quadrature approximation for some semilinear parabolic problems and give semidiscrete (space discretization) error analysis based on nonlinear semigroup techniques and Sobolev imbeddings. Optimal convergence rates are given for both smooth and nonsmooth data and with solution and gradient depending nonlinearities.
Mathematical Models and Methods in Applied Sciences, 1992
We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arisin... more We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.
Mathematical Models and Methods in Applied Sciences, 2007
We analyze the hp-version of the streamline diffusion finite element method for the Vlasov–Fokker... more We analyze the hp-version of the streamline diffusion finite element method for the Vlasov–Fokker–Planck system. For this method we prove the stability estimates and derive sharp a priori error bounds in a stabilization parameter δ ~ min (h/p, h2/σ), with h denoting the mesh size of the finite element discretization in phase-space-time, p the spectral order of approximation, and σ the transport cross-section.
Computer Methods in Applied Mechanics and Engineering, 2002
We consider a Fermi pencil-beam model in two-space dimensions ðx; yÞ, where x is aligned with the... more We consider a Fermi pencil-beam model in two-space dimensions ðx; yÞ, where x is aligned with the beam's penetration direction and y together with the scaled angular variable z correspond to a, bounded symmetric, transversal cross-section. The model corresponds to a forward-backward degenerate, convection dominated, convection-diffusion problem. For this problem we study some fully discrete numerical schemes using the standard-and Petrov-Galerkin finite element methods, for discretizations of the transversal domain, combined with the backward Euler, Crank-Nicolson, and discontinuous Galerkin methods for discretizations in the penetration variable. We derive stability estimates for the semi-discrete problems. Further, assuming sufficiently smooth exact solution, we obtain optimal a priori error bounds in a triple norm. These estimates give rise to a priori error estimates in the L 2-norm. Numerical implementations presented for some examples with the data approximating Dirac d function, confirm the expected performance of the combined schemes.
and discrete ordinates approximations for neutron transport equation and the critical eigenvalue ... more and discrete ordinates approximations for neutron transport equation and the critical eigenvalue M. ASADZADEH
Abstract. We give a survey of computational algorithms derived in a series of papers for solution... more Abstract. We give a survey of computational algorithms derived in a series of papers for solution of a synthesis problem for optimal stabilization of periodic systems. The proposed algorithms synthesize reliable control, with a given stability tolerance, for periodic systems optimized with respect to the quadratic performance criterion. A reliable controller guarantees the stability and is nearly a linear/quadratic regulator. We also consider the inverse problems for optimal synthesis corresponding to quadratic functionals. The algorithms designed to solve this problem are based on methods of linear matrix inequalities. The efficiency of the proposed algorithms are shown through implementing some examples. In this note we give an overview of computational algorithms for solution of a synthesis problem for optimal stabilization of periodic systems. Our study is based on stability of a discrete algebraic Riccati equation (ARE). The main feature of this study is to define an optimal re...
The paper considers the convergence study of the stabilized P1 finite element method for the time... more The paper considers the convergence study of the stabilized P1 finite element method for the time harmonic Maxwell’s equations. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. For the stabilized model a coercivity relation is derived that guarantee’s the existence of a unique solution for the discrete problem. The convergence is addressed both in a priori and a posteriori settings. Our numerical examples validate obtained convergence results.
This note is a study of combined Daubechies (Db2) wavelet transform and the statistical parameter... more This note is a study of combined Daubechies (Db2) wavelet transform and the statistical parameters skewness and kurtosis applied to detection of microcalcification in mammography. We have succintly introduced the concept of vanishing moments and derived scaling and wavelet functions using generating functions. The efficiency of the discrete algorithm is heavily relied on the order of performing wavelet approximation and the statistical procedure. The vital importance of both wavelet and statistical parameter approaches as well as the ordering issue in performing the analysis are justified through implementing numerical examples for some clinical data.
Abstract. This paper presents a nonstandard local approach to Richardson extrapolation, when it i... more Abstract. This paper presents a nonstandard local approach to Richardson extrapolation, when it is used to increase the accuracyof the standard finite element approximation of solutions of second order elliptic boundaryvalue problems in ℝ
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