Browsing by Subject "resonances"
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Item Analysis of a PML method applied to computation to resonances in open systems and acoustic scattering problems(2010-01-14) Kim, SeungilWe consider computation of resonances in open systems and acoustic scattering problems. These problems are posed on an unbounded domain and domain truncation is required for the numerical computation. In this paper, a perfectly matched layer (PML) technique is proposed for computation of solutions to the unbounded domain problems. For resonance problems, resonance functions are characterized as improper eigenfunction (non-zero solutions of the eigenvalue problem which are not square integrable) of the Helmholtz equation on an unbounded domain. We shall see that the application of the spherical PML converts the resonance problem to a standard eigenvalue problem on the infinite domain. Then, the goal will be to approximate the eigenvalues first by replacing the infinite domain by a finite computational domain with a convenient boundary condition and second by applying finite elements to the truncated problem. As approximation of eigenvalues of problems on a bounded domain is classical [12], we will focus on the convergence of eigenvalues of the (continuous) PML truncated problem to those of the infinite PML problem. Also, it will be shown that the domain truncation does not produce spurious eigenvalues provided that the size of computational domain is sufficiently large. The spherical PML technique has been successfully applied for approximation of scattered waves [13]. We develop an analysis for the case of a Cartesian PML application to the acoustic scattering problem, i.e., solvability of infinite and truncated Cartesian PML scattering problems and convergence of the truncated Cartesian PML problem to the solution of the original solution in the physical region as the size of computational domain increases.Item Investigation of electron-atom/molecule scattering resonances using complex multiconfigurational self-consistent field method(2010-07-14) Samanta, KousikWe present a complex multicon figurational self-consistent field (CMCSCF)- based approach to investigate electron{atom/molecule scattering resonances. A modifi ed second quantization algebra adapted for biorthogonal spin orbitals has been applied to develop a quadratically convergent CMCSCF scheme. A new step-length control algorithm has been introduced in order to control the walk on the complex energy hypersurface and converge to correct CMCSCF stationary point. We have also developed a method (M1 method) based on the multiconfigurational spin tensor electron propagator (MCSTEP) to calculate resonance energies directly. These methods have been applied to investigate atomic and molecular scattering resonances. The test cases for our application were 2^P Be- and 2II_g N-_2 shape resonances. The position and the width of these resonances have been calculated for different complete active space choices. Convergence for CMCSCF calculations to a tolerance of 1:0 x 10^-10 a.u. for the energy gradient is achieved typically within ten iterations or less. The wide distribution of the values for the position and the width of the resonance reported in the literature has been explained by showing that there actually exists two distinct resonances which are close in energy. The resonance positions and widths from our calculation for the 2^IIg N-_2 shape resonance have been found to be very close to the experimental results. In another study, the effect of the orbitals with higher angular momentum has been investigated.