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Second Order Multigrid Methods for Elliptic Problems with Discontinuous Coefficients on an Arbitrary Interface, I: One Dimensional Problems

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Numerical Mathematics(Theory,Methods and Applications) 2012年第1期5卷 19-42页

作者： Armando Coco giovanni russo Dipartimento di Matematica e Informatica Universitàdi CataniaViale Andrea Doria695125CataniaItaly

In this paper we present a one dimensional second order accurate method to solve Elliptic equations with discontinuous coefficients on an arbitrary *** order accuracy for the first derivative is obtained as *** method is based on the Ghost Fluid Method,making use of ghost points on which the value is defined by suitable interface *** multi-domain formulation is adopted,where the problem is split in two sub-problems and interface conditions will be enforced to close the *** conditions are relaxed together with the internal equations(following the approach proposed in[10]in the case of smooth coefficients),leading to an iterative method on all the set of grid values(inside points and ghost points).A multigrid approach with a suitable definition of the restriction operator is *** restriction of the defect is performed separately for both sub-problems,providing a convergence factor close to the one measured in the case of smooth coefficient and independent on the magnitude of the jump in the *** tests will confirm the second order *** the method is proposed in one dimension,the extension in higher dimension is currently underway[12]and it will be carried out by combining the discretization of[10]with the multigrid approach of[11]for Elliptic problems with non-eliminated boundary conditions in arbitrary domain.

关键词： Elliptic equation discontinuous coefficient second order accuracy multigrid arbitrary interface jump conditions

A High-Order Semi-Lagrangian Finite Difference Method for Nonlinear Vlasov and BGK Models

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Communications on Applied Mathematics and Computation 2023年第1期5卷 170-198页

作者： Linjin Li Jingmei Qiu giovanni russo Department of Mathematical Sciences University of DelawareNewarkDE 19717USA Department of Mathematics and Computer Science University of CataniaCataniaItaly

In this paper,we propose a new conservative high-order semi-Lagrangian finite difference(SLFD)method to solve linear advection equation and the nonlinear Vlasov and BGK *** finite difference scheme has better computational flexibility by working with point values,especially when working with high-dimensional problems in an operator splitting *** reconstruction procedure in the proposed SLFD scheme is motivated from the SL finite volume *** particular,we define a new sliding average function,whose cell averages agree with point values of the underlying *** developing the SL finite volume scheme for the sliding average function,we derive the proposed SLFD scheme,which is high-order accurate,mass conservative and unconditionally stable for linear *** performance of the scheme is showcased by linear transport applications,as well as the nonlinear Vlasov-Poisson and BGK ***,we apply the Fourier stability analysis to a fully discrete SLFD scheme coupled with diagonally implicit Runge-Kutta(DIRK)method when applied to a stiff two-velocity hyperbolic relaxation *** stability and asymptotic accuracy properties of DIRK methods are discussed in theoretical and computational aspects.

关键词： Semi-Lagrangian WENO Finite difference Vlasov-Poisson BGK equation Linear stability

ASecond-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries

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Communications in Computational Physics 2018年第1期23卷 230-263页

作者： Alina Chertock Armando Coco Alexander Kurganov giovanni russo Department of Mathematics North Carolina State UniversityRaleighNC 27695USA Department of Mechanical Engineering and Mathematical Sciences Oxford Brookes UniversityOxford OX331HXUK Department of Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China and Mathematics DepartmentTulane UniversityNew OrleansLA 70118USA Dipartimento diMatematica ed Informatica Universit`a di Catania95125CataniaItaly.

In this paper,we describe how to construct a finite-difference shockcapturing method for the numerical solution of the Euler equation of gas dynamics on arbitrary two-dimensional domainΩ,possibly with moving *** boundaries of the domain are assumed to be changing due to the movement of solid objects/obstacles/*** the motion of the boundary could be coupled with the fluid,all of the numerical tests are performed assuming that such a motion is prescribed and independent of the fluid *** method is based on discretizing the equation on a regular Cartesian grid in a rectangular domainΩ_(R)⊃Ω.Ωe identify inner and ghost *** inner points are the grid points located insideΩ,while the ghost points are the grid points that are outsideΩbut have at least one neighbor insideΩ.The evolution equations for inner points data are obtained from the discretization of the governing equation,while the data at the ghost points are obtained by a suitable extrapolation of the primitive variables(density,velocities and pressure).Particular care is devoted to a proper description of the boundary conditions for both fixed and time dependent *** numerical experiments are conducted to illustrate the validity of themethod.Ωe demonstrate that the second order of accuracy is numerically assessed on genuinely two-dimensional problems.

关键词： Compressible fluids Euler equations of gas dynamics ghost-cell extrapolation moving boundaries finite-difference shock-capturing methods

A Second Order Finite-Difference Ghost-Point Method for Elasticity Problems on Unbounded Domains with Applications to Volcanology

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Communications in Computational Physics 2014年第9期16卷 983-1009页

作者： Armando Coco Gilda Currenti Ciro Del Negro giovanni russo Dipartimento di Scienze della Terra e Geoambientali Universita di Bari Aldo MoroBariItaly. Bristol University Queens RoadBristol BS81RJUnited Kingdom. Istituto Nazionale di Geofisica e Vulcanologia Italy. Dipartimento di Matematica e Informatica Universita di CataniaCataniaItaly

We propose a finite-difference ghost-point approach for the numerical solution of Cauchy-Navier equations in linear elasticity problems on arbitrary unbounded *** technique is based on a smooth coordinate transformation,which maps an unbounded domain into a unit *** geometries are defined by suitable level-set *** equations are discretized by classical nine-point stencil on interior points,while boundary conditions and high order reconstructions are used to define the field variables at ghost-points,which are grid nodes external to the domain with a neighbor inside the *** linear system arising from such discretization is solved by a multigrid *** approach is then applied to solve elasticity problems in volcanology for computing the displacement caused by pressure *** method is suitable to treat problems in which the geometry of the source often changes(explore the effects of different scenarios,or solve inverse problems in which the geometry itself is part of the unknown),since it does not require complex re-meshing when the geometry is *** numerical tests are successfully performed,which asses the effectiveness of the present approach.

关键词： Linear elasticity Cauchy-Navier equations ground deformation unbounded domain coordinate transformation method Cartesian grid ghost points level-set methods multigrid.

High Order Conservative Semi-Lagrangian Scheme for the BGK Model of the Boltzmann Equation

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Communications in Computational Physics 2021年第1期29卷 1-56页

作者： Sebastiano Boscarino Seung-Yeon Cho giovanni russo Seok-Bae Yun Department of Mathematics and Computer Science University of Catania95125 CataniaItaly Department of Mathematics Sungkyunkwan UniversitySuwon 440-746Republic of Korea

In this paper,we present a conservative semi-Lagrangian finite-difference scheme for the BGK *** semi-Lagrangian finite difference schemes,coupled with an L-stable treatment of the collision term,allow large time steps,for all the range of Knudsen number[17,27,30].Unfortunately,however,such schemes are not *** of conservation is analyzed in detail,and two main sources are identified as its ***,when using classical continuous Maxwellian,conservation error is negligible only if velocity space is resolved with sufficiently large number of grid ***,for a small number of grid points in velocity space such error is not negligible,because the parameters of the Maxwellian do not coincide with the discrete ***,the non-linear reconstruction used to prevent oscillations destroys the translation invariance which is at the basis of the conservation properties of the *** a consequence the schemes show a wrong shock speed in the limit of small Knudsen *** treat the first problem and ensure machine precision conservation of mass,momentum and energy with a relatively small number of velocity grid points,we replace the continuous Maxwellian with the discrete Maxwellian introduced in[22].The second problem is treated by implementing a conservative correction procedure based on the flux difference form as in[26].In this way we can construct conservative semi-Lagrangian schemes which are Asymptotic Preserving(AP)for the underlying Euler limit,as the Knudsen number *** effectiveness of the proposed scheme is demonstrated by extensive numerical tests.

关键词： BGK model Boltzmann equation semi-Lagrangian scheme conservative correction discrete Maxwellian

Anomalous Sorption Kinetics of Self-Interacting Particles by a Spherical Trap

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Communications in Computational Physics 2022年第3期31卷 707-738页

作者： Antonio Raudino Antonio Grassi Giuseppe Lombardo giovanni russo Clarissa Astuto Mario Corti Department of Chemical Sciences University of CataniaViale A.Doria 6-95125CataniaItaly Department of Mathematics University of CataniaViale A.Doria 6-95125 CataniaItaly Applied Mathematics and Computational Science King Abdullah University of Science and Technology(KAUST)4700ThuwalSaudi Arabia CNR-IPCF Viale F.Stagno d’Alcontres 3798158 MessinaItaly

In this paper we propose a computational framework for the investigation of the correlated motion between positive and negative ions exposed to the attraction of a bubble surface that mimics the(oscillating)cell *** we aim to investigate the role of surface traps with substances freely diffusing around the *** physical system we want to model is an anchored gas drop submitted to a diffusive flowof charged surfactants(ions).When the diffusing surfactantsmeet the surface of the bubble,they are reversibly adsorbed and their local concentration is accurately *** correlated diffusion of surfactants is described by a Poisson-Nernst-Planck(PNP)system,in which the drift term is given by the gradient of a potential which includes both the effect of the bubble and the Coulomb interaction between the *** latter term is obtained from the solution of a self-consistent Poisson *** very short Debye lengths one can adopt the so called Quasi-Neutral limit which drastically simplifies the system,thus allowing for much faster numerical *** paper has four main *** first one is to present a PNP model that describes ion charges in presence of a *** second one is to provide benchmark tests for the validation of simplified multiscale models under current development[1].The third one is to explore the relevance of the term describing the interaction among the apolar tails of the *** last one is to quantitatively explore the validity of the Quasi-Neutral limit by comparison with detailed numerical simulation for smaller and smaller Debye *** order to reach these goals,we propose a simple and efficient Alternate Direction Implicit method for the numerical solution of the non-linear PNP system,which guarantees second order accuracy both in space and time,without requiring solution of nonlinear equation at each time *** semi-implicit scheme for a simplified PNP system near quasi neutrality is also p

关键词： Spherycal trap quasi-neutrality finite differences Coulomb potential Poisson-Nernst-Planck system ADI discretization semi-implicit scheme

The Palmanova Cantonments： Conservation, Value-Enhancement and Transformation for an Integrated and Overall Regeneration

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Journal of Civil Engineering and Architecture 2017年第6期11卷 559-570页

作者： Maria Paola Gatti giovanni russo Luca Zecchin Department of CiviL Environmental and Mechanical Engineering University of Trento Trento 38123 Italy

Italian military real-estate is highly varied as regards its location, intended uses, its typological, stylistic, and constructive features and its state of conservation. What historical and documental value can we attribute to the typological and technical aspects of military buildings？ What problems and strategies have to be studied before such buildings can be repurposed for inclusion into a circuit of social and civil uses？ Some attempts were made to answer these questions by analysing the military real estate of Palmanova, the fortress city founded by the Serenissima Republic of Venice in 1593, a city designed by engineers, military analysts, and expert military architects all answerable to the Fortifications Office of Venice. There are a number of barracks situated inside the city＇s fortified walls, within a somewhat confined area： Montezemolo, Isonzo, Ederle, Filzi, Montesanto and others in outlying villages. Barracks built in different periods （some during the Renaissance, others in the eighteenth century and some even after the Second World War） have been gradually phased out of service. Their restoration and functional leverage, in the early years of this century, were discussed in terms of an economic and cultural strategy that would not upset the city. New regeneration strategies are called for if these abandoned military structures are not to undergo further deterioration. These strategies should be based upon a knowledge of these structures＇ features--their layout, architecture, technologies--and should also embrace local policies, but first and foremost they require real, contextualized and economically sustainable projects.

关键词： Fortress decommissioning securitization value-enhancement conservation regeneration.

Preface to Focused Section on Efficient High-Order Time Discretization Methods for Partial Differential Equations

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Communications on Applied Mathematics and Computation 2021年第4期3卷 605-605页

作者： Sebastiano Boscarino Giuseppe Izzo Lorenzo Pareschi giovanni russo Chi-Wang Shu Universita degli Studi di Catania 95131 CataniaItaly Universita degli Studi di Napoli Federico II 80126 NaplesItaly Universita degli Studi di Ferrara 44121 FerraraItaly Brown University ProvidenceRI02912USA

During May 8-10,2019,the International Workshop on Efficient High-Order Time Discretization Methods for Partial Differential Equations took place in Villa Orlandi,Anacapri,Italy,a Congress Center of the University of Naples Federico *** 40 senior researchers,young scholars,and *** attended this *** purpose of this event was to explore recent trends and directions in the area of time discretization for the numerical solution of evolutionary partial differential equations with particular application to high-order methods for hyperbolic systems with source and advection-diffusion-reaction equations,and with special emphasis on efficient time-stepping methods such as implicit-explicit(IMEX),semi-implicit and strong stability preserving(SSP)time *** present focused section entitled“Efficient High-Order Time Discretization Methods for Partial Differential Equations”in Communications on Applied Mathematics and Computation(CAMC)consists of five regularly reviewed manuscripts,which were selected from submissions of works presented during the *** thank all the authors of these contributions,and hope that the readers are interested in the topics,techniques and methods,and results of these *** also want to thank the CAMC journal editorial staff as well as all the referees for their contributions during the review and publication processes of this focused section.

关键词： thank hyperbolic preserving

Groups with Finitely Many Homomorphic Images of Finite Rank

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Algebra Colloquium 2016年第2期23卷 181-187页

作者： Francesco de giovanni Alessio russo Dipartimento di Matematica e Applicazioni Universitg di Napoli Federico II Complesso Universitario Monte S. Angelo Via Cintia 1-80126 Napoli Italy Dipartimento di Matematica e Fisica Seconda Universitg di Napoli Via Lincoln 5 1-81100 Caserta Italy

A group is called a Cernikov group if it is abelian-by-finite and satisfies the minimal condition on subgroups. A new characterization of Cernikov groups is given here, by proving that in a suitable large class of generalised soluble groups they coincide with the groups having only finitely many homomorphic images of finite rank （up to isomorphisms） and admitting an ascending normal series whose factors have finite rank.

关键词： Prufer rank Cernikov group homomorphic image