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### A NUMERICAL STUDY OF HIERARCHICAL MATRIX (H-MATRIX) FOR FINITE POINT SET METHOD (FPM) ON SOLVING A POISSON PROBLEM

S. Gedela, S. Sundar
2013 International Journal of Applied Mathematics
A class of matrices called H-matrices is used to approximate large matrices of grid based methods. H-matrix arithmetic has linear-logarithmic complexity for some special grids.  ...  In this paper, we present a study on Hmatrix for a large sparse un-patterned system arising from a grid free method called finite pointset method applied on a Poisson problem with mixed boundary conditions  ...  [11] have studied H-matrix methods for linear and quasi-linear integral operators appearing in population balances and obtained linear complexity for matrix arithmetic.  ...

### Page 2898 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews
Mechanisms for the generation of mesoscale vortices within quasi-linear convective systems.  ...  Summary: “In this paper we consider a piecewise bilinear colloca- tion method for the solution of a singular integral equation over a part of the surface of the earth.  ...

### Reducing nonlinear dynamical systems to canonical forms

Léon Brenig
2018 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
It consists in the difference between the commutators [B i , A j ] = δ ij B j appearing in the LV algebra, and the commutators [B i , A j ] = δ ij for the linear algebra.  ...  The N × N matrix M is called the population interaction matrix.  ...

### Invariance correction to Grad's equations: where to go beyond approximations?

Alexander N. Gorban, Iliya V. Karlin
2005 Continuum Mechanics and Thermodynamics
Relations of Grad's approach to modern mesoscopic integrators such as the entropic lattice Boltzmann method are also discussed.  ...  A consistent derivation of regularized Grad's equations in the framework the method of invariant manifold is given.  ...  Ansumali for his contributions to Sect. 4, and for providing the figures.  ...

### A fast boundary element method for the solution of periodic many-inclusion problems via hierarchical matrix techniques

Paul Cazeaux, Olivier Zahm, Nicolas Champagnat, Tony Lelièvre, Anthony Nouy
2015 ESAIM Proceedings and Surveys
The fully populated matrices obtained by the discretization of the integral operators are successfully dealt with using the H-matrix format. Résumé.  ...  In this paper, we propose a method for the approximation of the periodic corrector problem based on boundary integral equations.  ...  In the following, we present the classical procedure for the approximation of an integral operator in the H-matrix format [5] .  ...

### Constructive methods of invariant manifolds for kinetic problems

A GORBAN
2004 Physics reports
Among them, iteration methods based on incomplete linearization, relaxation method and the method of invariant grids are developed.  ...  We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades.  ...  Linearized collision integral Linearization of the Boltzmann integral around the local equilibrium results in the linear integral operator, Lh(C) = W (C; w | C ; w )f LM (C)f LM (w) h(C ) f LM (C ) + h  ...

### Constructive methods of invariant manifolds for kinetic problems

Alexander N. Gorban, Iliya V. Karlin, Andrei Yu. Zinovyev
2004 Physics reports
We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades.  ...  A collection of methods for construction of slow invariant manifolds is presented, in particular the analogue of KAM methods for dissipative systems.  ...  Linearized collision integral Linearization of the Boltzmann integral around the local equilibrium results in the linear integral operator, Lh(C) = W (C; w | C ; w )f LM (C)f LM (w) h(C ) f LM (C ) + h  ...

### Similarities between the quasi-bubble and the generalized wave continuity equation solutions to the shallow water equations

J. H. Atkinson, J. J. Westerink, J. M. Hervouet
2004 International Journal for Numerical Methods in Fluids
In this work, the quasi-bubble equations are analysed and comparisons are made between the quasi-bubble approximation of the primitive form of the shallow water equations and a linear ÿnite element approximation  ...  Two common strategies for solving the shallow water equations in the ÿnite element community are the generalized wave continuity equation (GWCE) reformulation and the quasi-bubble velocity approximation  ...  Using the operator notation of Kinnmark [3] , the linearized continuity and momentum equations are deÿned by the following notation: L ≡ @ @t + h @u @x + @v @y = 0 (1) M x ≡ @u @t + u + g @ @x = 0 (2)  ...

### Reactor Network Synthesis Using Coupled Genetic Algorithm with the Quasi-linear Programming Method english

H. Soltani
2016 Chemical and Biochemical Engineering Quarterly
genetic algorithm (GA) coupled with the quasi-linear programming (LP) method.  ...  c Offshore production supervisor Pars oil and gas company (POGC) operation unit, Tehran, Iran This research is an attempt to develop a new procedure for the synthesis of reactor networks (RNs) using a  ...  This paper addresses the problem of the synthesis of RNs using a combination of genetic algorithm and quasi-linear programming (LP) method, in which GA, with the help of its operators (i.e. reproduction  ...

### Population balance modelling and H∞—controller design for a crystallization process

Ulrich Vollmer, Jörg Raisch
2002 Chemical Engineering Science
A detailed population balance model for the process can be found in the literature. Based on this detailed model we develop a simpler population balance model.  ...  An H∞ mixed sensitivity minimization problem is formulated and solved using an innite-dimensional version of H∞ theory. Two dierent controllers are designed and compared in simulation studies. ?  ...  This leadsafter some restructuring-to the following linear process model: Population balance With the piecewise linear expressions for the growth rates (14) and (15) the integrals in the above equations  ...

### A partially linearized spin-mapping approach for nonadiabatic dynamics. I. Derivation of the theory [article]

J. R. Mannouch, J. O. Richardson
2020 arXiv   pre-print
These new features appear to give the method superior accuracy for computing dynamical observables of interest, when compared with other methods within the same class.  ...  We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called spin-PLDM.  ...  We also thank Johan Runeson for helpful discussions and for his comments made on the original manuscript.  ...

### Resolution-of-identity stochastic time-dependent configuration interaction for dissipative electron dynamics in strong fields

2016 Journal of Chemical Physics
In this contribution, we introduce a method for simulating dissipative, ultrafast many-electron dynamics in intense laser fields.  ...  The method finds its efficiency in the representation of the operators in the interaction picture, where the resolution-of-identity is used to reduce the size of the Hamiltonian eigenstate basis.  ...  For the ground state population, the final value is found in a range between 0.10 and 0.15.  ...

### Model Photospheres with Accelerated Lambda Iteration [article]

K. Werner, J.L. Deetjen, S. Dreizler, T. Nagel, T. Rauch, S.L. Schuh
2002 arXiv   pre-print
We address the classical stellar-atmosphere problem and describe our method of numerical solution in detail.  ...  We employ the Accelerated Lambda Iteration (ALI) technique, and use statistical methods to construct non-LTE metal-line-blanketed model-atmospheres.  ...  Each matrix inversion in Eq. 6 requires (N L + 4) 3 operations whereas in the CL method (N L + N F + 4) 3 operations are needed.  ...

### Quantum initial condition sampling for linearized density matrix dynamics: Vibrational pure dephasing of iodine in krypton matrices

Z. Ma, D. F. Coker
2008 Journal of Chemical Physics
This paper reviews the linearized path integral approach for computing time dependent properties of systems that can be approximated using a mixed quantum-classical description.  ...  This approach is applied to studying vibrational pure dephasing of ground state molecular iodine in a rare gas matrix.  ...  In this case there is no population relaxation between our vibrational basis states so the propagator matrix elements appearing in Eq.(1) can be written in the composite bath subsystem path integral forms  ...

### Nested Decomposition Approach for Dispatch Optimization of Large-Scale, Integrated Electricity, Methane and Hydrogen Infrastructures

Lukas Löhr, Raphael Houben, Carolin Guntermann, Albert Moser
2022 Energies : open-access journal of related scientific research
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY  ...  • Remaining model simplifications like DC power flow, quasi-steady-state gas flow, a rough estimation of contingencies and the neglect of non-linear operating constraints, but they appear to be largely  ...  Figure 1 shows the population of the coefficient matrix of the linearized integrated dispatch problem in full technical detail (see Section 2.7) when applied to the European scenario.  ...
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