Relevant bibliographies by topics / Particle methods (Numerical analysis)

Academic literature on the topic 'Particle methods (Numerical analysis)'

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Published: 4 June 2021
Last updated: 26 January 2023

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Particle methods (Numerical analysis)":

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Neunzert, Helmut, and Jens Struckmeier. "Particle Methods for the Boltzmann Equation." Acta Numerica 4 (January 1995): 417–57. http://dx.doi.org/10.1017/s0962492900002579.

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In the following chapters we will discuss particle methods for the numerical simulation of rarefied gas flows.We will mainly treat a billiard game, that is, our particles will be hard spheres. But we will also touch upon cases where particles have internal energies due to rotation or vibration, which they exchange in a collision, and we will talk about chemical reactions happening during a collision.Due to the limited size of this paper, we are only able to mention the principles of these real-gas effects. On the other hand, the general concepts of particle methods to be presented may be used for other kinds of kinetic equations, such as the semiconductor device simulation. We leave this part of the research to subsequent papers.
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KOSHIZUKA, Seiichi. "Numerical Analysis of Continuous Media Using Particle Methods." JOURNAL OF THE JAPAN WELDING SOCIETY 75, no. 2 (2006): 126–28. http://dx.doi.org/10.2207/jjws.75.126.

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Bagtzoglou, Amvrossios C., Andrew F. B. Tompson, and David E. Dougherty. "Projection functions for particle-grid methods." Numerical Methods for Partial Differential Equations 8, no. 4 (July 1992): 325–40. http://dx.doi.org/10.1002/num.1690080403.

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Havlak, Karl J., and Harold Dean Victory. "On Deterministic Particle Methods for Solving Vlasov--Poisson--Fokker--Planck Systems." SIAM Journal on Numerical Analysis 35, no. 4 (August 1998): 1473–519. http://dx.doi.org/10.1137/s0036142996302529.

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Wollman, Stephen. "On the Approximation of the Vlasov--Poisson System by Particle Methods." SIAM Journal on Numerical Analysis 37, no. 4 (January 2000): 1369–98. http://dx.doi.org/10.1137/s0036142999298528.

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Ganguly, Keshab, and H. D. Victory, Jr. "On the Convergence of Particle Methods for Multidimensional Vlasov–Poisson Systems." SIAM Journal on Numerical Analysis 26, no. 2 (April 1989): 249–88. http://dx.doi.org/10.1137/0726015.

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Draghicescu, C. I. "An Efficient Implementation of Particle Methods for the Incompressible Euler Equations." SIAM Journal on Numerical Analysis 31, no. 4 (August 1994): 1090–108. http://dx.doi.org/10.1137/0731057.

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Patterson, Robert I. A., and Wolfgang Wagner. "Cell Size Error in Stochastic Particle Methods for Coagulation Equations with Advection." SIAM Journal on Numerical Analysis 52, no. 1 (January 2014): 424–42. http://dx.doi.org/10.1137/130924743.

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Guo, Meizhai, Megan S. Lord, and Zhongxiao Peng. "Quantitative wear particle analysis for osteoarthritis assessment." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 231, no. 12 (October 5, 2017): 1116–26. http://dx.doi.org/10.1177/0954411917735081.

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Osteoarthritis is a degenerative joint disease that affects millions of people worldwide. The aims of this study were (1) to quantitatively characterise the boundary and surface features of wear particles present in the synovial fluid of patients, (2) to select key numerical parameters that describe distinctive particle features and enable osteoarthritis assessment and (3) to develop a model to assess osteoarthritis conditions using comprehensive wear debris information. Discriminant analysis was used to statistically group particles based on differences in their numerical parameters. The analysis methods agreed with the clinical osteoarthritis grades in 63%, 50% and 61% of particles for no osteoarthritis, mild osteoarthritis and severe osteoarthritis, respectively. This study has revealed particle features specific to different osteoarthritis grades and provided further understanding of the cartilage degradation process through wear particle analysis – the technique that has the potential to be developed as an objective and minimally invasive method for osteoarthritis diagnosis.
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Victory, Jr., H. D., Garry Tucker, and Keshab Ganguly. "The Convergence Analysis of Fully Discretized Particle Methods for Solving Vlasov–Poisson Systems." SIAM Journal on Numerical Analysis 28, no. 4 (August 1991): 955–89. http://dx.doi.org/10.1137/0728051.

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You might also be interested in the extended bibliographies on the topic 'Particle methods (Numerical analysis)' for particular source types:
Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Particle methods (Numerical analysis)":

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Shanmugam, Bala Priyadarshini. "Investigation of kernels for the reproducing kernel particle method." Birmingham, Ala. : University of Alabama at Birmingham, 2009. https://www.mhsl.uab.edu/dt/2009m/shanmugam.pdf.

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Yang, Weixuan. "Temperature-dependent homogenization technique and nanoscale meshfree particle methods." Diss., University of Iowa, 2007. http://ir.uiowa.edu/etd/147.

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Bunch, Peter Joseph. "Particle filtering and smoothing for challenging time series models." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708151.

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Borovies, Drew A. "Particle filter based tracking in a detection sparse discrete event simulation environment." Thesis, Monterey, Calif. : Naval Postgraduate School, 2007. http://bosun.nps.edu/uhtbin/hyperion.exe/07Mar%5FBorovies.pdf.

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Thesis (M.S. in Modeling, Virtual Environment, and Simulation (MOVES))--Naval Postgraduate School, March 2007.
Thesis Advisor(s): Christian Darken. "March 2007." Includes bibliographical references (p. 115). Also available in print.
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Bhojwani, Shekhar. "Smoothed particle hydrodynamics modeling of the friction stir welding process." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2007. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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Piqueras, García Miguel Ángel. "Numerical Methods for Multidisciplinary Free Boundary Problems: Numerical Analysis and Computing." Doctoral thesis, Universitat Politècnica de València, 2018. http://hdl.handle.net/10251/107948.

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Multitud de problemas en ciencia e ingeniería se plantean como ecuaciones en derivadas parciales (EDPs). Si la frontera del recinto donde esas ecuaciones han de satisfacerse se desconoce a priori, se habla de "Problemas de frontera libre", propios de sistemas estacionarios no dependientes del tiempo, o bien de "Problemas de frontera móvil", asociados a problemas de evolución temporal, donde la frontera cambia con el tiempo. La solución a dichos problemas viene dada por la expresión de la(s) variable(s) dependiente(s) de la(s) EDP(s) junto con la función que determina la posición de la frontera. Dado que este tipo de problemas carece en la mayoría de los casos de solución analítica conocida, se hace preciso recurrir a métodos numéricos que permitan obtener una solución lo suficientemente aproximada, y que además mantenga propiedades cualitativas de la solución del modelo continuo de EDP(s). En este trabajo se ha abordado el estudio numérico de algunos problemas de frontera móvil provenientes de diversas disciplinas. La metodología aplicada consta de dos pasos sucesivos: aplicación de la transformación de Landau o "Front-fixing transformation" al modelo en EDP(s) con el fin de mantener inmóvil la frontera del dominio, y posterior discretización a través de un esquema en diferencias finitas. De ahí se obtienen esquemas numéricos que se implementan por medio de la herramienta MATLAB. Mediante un exhaustivo análisis numérico, se estudian propiedades del esquema y de la solución numérica (positividad, estabilidad, consistencia, monotonía, etc.). En el primer capítulo de este trabajo se revisa el estado del arte del campo objeto de estudio, se justifica la necesidad de disponer de métodos numéricos adaptados a este tipo de problemas y se describe brevemente la metodología empleada en nuestro enfoque. El Capítulo 2 se dedica a un problema perteneciente a la Biología Matemática y que consiste en determinar la evolución de la población de una especie invasora que se propaga en un hábitat. Este modelo consiste en una ecuación de difusión-reacción unida a una condición tipo Stefan. Los resultados del análisis numérico confirman la existencia de una dicotomía propagación-extinción en la evolución a largo plazo de la densidad de población de la especie invasora. En particular, se ha podido precisar el valor del coeficiente de la condición de Stefan que separa el comportamiento de propagación del de extinción. Los Capítulos 3 y 4 se centran en un problema de Química del Hormigón con interés en Ingeniería Civil: el proceso de carbonatación del hormigón, fenómeno evolutivo que lleva consigo la degradación progresiva de la estructura afectada y finalmente su ruina, si no se toman medidas preventivas. En el Capítulo 3 se considera un sistema de dos EDPs de tipo parabólico con dos incógnitas. Para su resolución, hay que considerar además las condiciones iniciales, las de contorno y las de tipo Stefan en la frontera. Los resultados numéricos confirman la tendencia de la ley de evolución de la frontera móvil hacia una función del tipo "raíz cuadrada del tiempo". En el Capítulo 4 se considera un modelo más general que el anterior, en el que intervienen seis especies químicas que se encuentran tanto en la zona carbonatada como en la no carbonatada. En el Capítulo 5 se aborda un problema de transmisión de calor que aparece en diversos procesos industriales; en este caso, en el enfriamiento durante la colada de metal fundido, donde la fase sólida avanza y la líquida se va extinguiendo. La frontera móvil (frente de solidificación) separa ambas fases, siendo su posición en cada instante la variable a determinar, junto con las temperaturas en cada fase. Después de la adecuada transformación y discretización, se implementa un esquema en diferencias finitas, subdividiendo el proceso en tres estadios temporales, a fin de tratar las singularidades asociadas a posicione
Many problems in science and engineering are formulated as partial differential equations (PDEs). If the boundary of the domain where these equations are to be solved is not known a priori, we face "Free-boundary problems", which are characteristic of non-time dependent stationary systems; besides, we have "Moving-boundary problems" in temporal evolution processes, where the border changes over time. The solution to these problems is given by the expression of the dependent variable(s) of PDE(s), together with the function that determines the position of the boundary. Since the analytical solution of this type of problems is lacked in most cases, it is necessary to resort to numerical methods that allow an accurate enough solution to be obtained, and which also maintain the qualitative properties of the solution(s) of the continuous model. This work approaches the numerical study of some moving-boundary problems that arise in different disciplines. The applied methodology consists of two successive steps: firstly, the so-called Landau transformation, or "Front-fixing transformation", which is used in the PDE(s) model to maintain the boundary of the domain immobile; later, we proceed to its discretization with a finite difference scheme. Different numerical schemes are obtained and implemented through the MATLAB computational tool. Properties of the scheme and the numerical solution (positivity, stability, consistency, monotonicity, etc.) are studied by an exhaustive numerical analysis. The first chapter of this work reports the state of the art of the field under study, justifies the need to adapt numerical methods to this type of problem, and briefly describes the methodology used in our approach. Chapter 2 presents a problem in Mathematical Biology that consists in determining over time the evolution of an invasive species population that spreads in a habitat. This problem is modelled by a diffusion-reaction equation linked to a Stefan-type condition. The results of the numerical analysis confirm the existence of a spreading-vanishing dichotomy in the long-term evolution of the population density of the invasive species. In particular, it is possible to determine the value of the coefficient of the Stefan condition that separates the propagation behaviour from extinction. Chapters 3 and 4 focus on a problem of Concrete Chemistry with an interest in Civil Engineering: the carbonation of concrete, an evolutionary phenomenon that leads to the progressive degradation of the affected structure and its eventual ruin if preventive measures are not taken. Chapter 3 considers a system of two parabolic type PDEs with two unknowns. For its resolution, the initial and boundary conditions have to be considered together with the Stefan conditions on the carbonation front. The numerical analysis results agree with those obtained in a previous theoretical study. The dynamics of the concentrations and the moving boundary confirm the long-term behaviour of the evolution law for the moving boundary as a "square root of time". Chapter 4 considers a more general model than the previous one, which includes six chemical species, defined in both the carbonated and non-carbonated zones, whose concentrations have to be found. Chapter 5 addresses a heat transfer problem that appears in various industrial processes; in this case, the solidification of metals in casting processes, where the solid phase advances and liquid reduces until it is depleted. The moving boundary (the solidification front) separates both phases. Its position in each instant is the variable to be determined together with the temperature profiles in both phases. After suitable transformation, discretization is carried out to obtain a finite difference scheme to be implemented. The process was subdivided into three temporal stages to deal with the singularities associated with the moving boundary position in the initialisation and depletion stages.
Multitud de problemes en ciència i enginyeria es plantegen com a equacions en derivades parcials (EDPs). Si la frontera del recinte on eixes equacions han de satisfer-se es desconeix a priori, es parla de "Problemas de frontera lliure", propis de sistemes estacionaris no dependents del temps, o bé de "Problemas de frontera mòbil", associats a problemes d'evolució temporal, on la frontera canvia amb el temps. Atés que este tipus de problemes manca en la majoria dels casos de solució analítica coneguda, es fa precís recórrer a mètodes numèrics que permeten obtindre una solució prou aproximada a l'exacta, i que a més mantinga propietats qualitatives de la solució del model continu d'EDP(s). En aquest treball s'ha abordat l'estudi numèric d'alguns problemes de frontera mòbil provinents de diverses disciplines. La metodologia aplicada consta de dos passos successius: en primer lloc, s'aplica l'anomenada transformació de Landau o "Front-fixing transformation" al model en EDP(s) a fi de mantindre immòbil la frontera del domini; posteriorment, es procedix a la seva discretització a través d'un esquema en diferències finites. D'ací s'obtenen esquemes numèrics que s'implementen per mitjà de la ferramenta informàtica MATLAB. Per mitjà d'una exhaustiva anàlisi numèrica, s'estudien propietats de l'esquema i de la solució numèrica (positivitat, estabilitat, consistència, monotonia, etc.). En el primer capítol d'aquest treball es revisa l'estat de l'art del camp objecte d'estudi, es justifica la necessitat de disposar de mètodes numèrics adaptats a aquest tipus de problemes i es descriu breument la metodologia emprada en el nostre enfocament. El Capítol 2 es dedica a un problema pertanyent a la Biologia Matemàtica i que consistix a determinar l'evolució en el temps de la distribució de la població d'una espècie invasora que es propaga en un hàbitat. Este model consistix en una equació de difusió-reacció unida a una condició tipus Stefan, que relaciona les funcions solució i frontera mòbil a determinar. Els resultats de l'anàlisi numèrica confirmen l'existència d'una dicotomia propagació-extinció en l'evolució a llarg termini de la densitat de població de l'espècie invasora. En particular, s'ha pogut precisar el valor del coeficient de la condició de Stefan que separa el comportament de propagació del d'extinció. Els Capítols 3 i 4 se centren en un problema de Química del Formigó amb interés en Enginyeria Civil: el procés de carbonatació del formigó, fenomen evolutiu que comporta la degradació progressiva de l'estructura afectada i finalment la seua ruïna, si no es prenen mesures preventives. En el Capítol 3 es considera un sistema de dos EDPs de tipus parabòlic amb dos incògnites. Per a la seua resolució, cal considerar a més, les condicions inicials, les de contorn i les de tipus Stefan en la frontera. Els resultats de l'anàlisi numèrica s'ajusten als obtinguts en un estudi teòric previ. S'han dut a terme experiments numèrics, comprovant la tendència de la llei d'evolució de la frontera mòbil cap a una funció del tipus "arrel quadrada del temps". En el Capítol 4 es considera un model més general, en el que intervenen sis espècies químiques les concentracions de les quals cal trobar, i que es troben tant en la zona carbonatada com en la no carbonatada. En el Capítol 5 s'aborda un problema de transmissió de calor que apareix en diversos processos industrials; en aquest cas, en el refredament durant la bugada de metall fos, on la fase sòlida avança i la líquida es va extingint. La frontera mòbil (front de solidificació) separa ambdues fases, sent la seua posició en cada instant la variable a determinar, junt amb les temperatures en cada una de les dos fases. Després de l'adequada transformació i discretització, s'implementa un esquema en diferències finites, subdividint el procés en tres estadis temporals, per tal de tractar les singularitats asso
Piqueras García, MÁ. (2018). Numerical Methods for Multidisciplinary Free Boundary Problems: Numerical Analysis and Computing [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/107948
TESIS
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Casas, González Guillermo. "Numerical analysis of particle-laden flows with the finite element method." Doctoral thesis, Universitat Politècnica de Catalunya, 2018. http://hdl.handle.net/10803/666324.

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In this work we study the numerical simulation of particle-laden fluids, with a focus on Newtonian fluids and spherical, rigid particles. We are thus dealing with a multi-phase (more precisely, a multi-component) problem, with two phases: the fluid (continuous phase) and the the particles (disperse phase). Our general strategy consists in using the discrete element method (DEM) to model the particles and the finite element method (FEM) to discretize the Navier-Stokes equations, which model the continuous phase. The interaction model between both phases is (must be) based on a multiscale concept, since the smallest scales resolved of the continuous phase are considered much bigger than the particles. In other words, the resolution of the numerical model for the particles is finer than that used for the fluid. Consequently, whether implicit or explicit, there must be a filtering or averaging operation involved in the interaction between both phases, where the details of their motions smaller than the smallest resolution scale of the fluid are soothed out, since the latter is the coarsest of the two different resolutions considered. The spatial discretization of the continuous phase is performed with the FEM, using equal-order spaces of shape functions for the velocity and for the pressure. It is a well-known fact that this type of combination involves the violation of the Ladyzenskaja-Babuška-Brezzi (LBB) condition, resulting in an unstable numerical method. Moreover, the presence of the convective term in Eulerian description of the flow also leads to numerical instabilities. Both effects are treated with the sub-grid scale stabilization methods here. About the disperse phase, the trajectory of each particle is calculated based both on the fluid-interaction forces and on the contact forces between them and the surrounding rigid boundaries. The differential equation that describes the motion of particles in between successive collisions, given the mean (averaged) far field and for particles much smaller than the smallest scales of the flow (the Kolmogorov scale in turbulence) is the Maxey-Riley equation (MRE). This equation is the subject of chapter 2. The objective of this theoretical study is to establish quantitative (up to order-of-magnitude accuracy) limits to its range of validity and to the relative importance of its various terms. The method employed is dimensional analysis, which is systematically applied to derive the 'first effects' of a series of phenomena that are neglected in the derivation of the MRE. Chapter 3 is dedicated to the numerical resolution of the MRE. Here we present improvements to the method of van Hinsberg et al. (2011) for the calculation of the history term and analyse the method thoroughly. We include several tests to show the efficiency and utility of the proposed approach. The MRE is directly applicable to flows where the particle-based Reynolds number is Re << 1. But its relevance reaches further, as its structure is the basis for the majority of extensions that model the movement of suspended particles outside the range of validity of the MRE. Chapter 4 is markedly more applied than the two preceding ones. It treats various industrial flux types with particles where we employ several extensions of the MRE of the type mentioned above. In the first part of this chapter we review the most important of these extensions and study the process of derivative recovery, necessary to calculate several terms in the equation of motion. The tests examples considered include bubble trapping in 'T'-junction tubes, the simulation of drilling systems of the oil industry based on the bombardment of steel particles and fluidized beds. For the latter we use a discrete filtering-based coupling approach, that mirrors the continuous theory sketched above. This set of three chapters (2, 3, 4) is the core of the Thesis, which is completed with an introduction (chapter 1) and the conclusions (chapter 5).
En este trabajo se estudia la simulación numérica de fluidos con partículas en suspensión, con énfasis en fluidos newtonianos y partículas esféricas y rígidas. El problema es, pues, multi-fásico (o, más precisamente, multi-componente) en donde dos son las fases: el fluido (fase continua) y las partículas (fase dispersa). La estrategia general consiste en la modelización de las partículas mediante el método de los elementos discretos (DEM) y el método de los elementos finitos (FEM) para la discretización de las ecuaciones de Navier-Stokes, que modelan la fase continua. El modelo de interacción entre fases se basa (debe basarse) en una concepción multiescala del sistema, puesto que las escalas más pequeñas resueltas para el fluido se consideran mucho mayores a las partículas. Dicho de otro modo, ya sea implícita o explícitamente, en la interacción interviene un proceso de filtrado o promediado en que se suavizan los detalles del movimiento más pequeños que la escala de resolución del fluido. Par la fase continua la discretización del dominio se realiza con el FEM, con espacios de funciones de forma de igual orden para la velocidad y para la presión. Como es bien sabido, ello conlleva la violación de la condición de Ladyzenskaja-Babuška-Brezzi (LBB), dando un método numérico inestable. Además, la presencia del término convectivo en la descripción euleriana del flujo también resulta en inestabilidad. Ambos son tratados con métodos de estabilización basada en la modelización de 'escalas sub-malla'. En cuanto a la fase dispersa, se calcula la trayectoria de cada una de las partículas en función de fuerzas de contacto con las demás partículas y las superficies sólidas que limitan el dominio de cálculo por un lado, y de las fuerzas de interacción con el fluido por otro. La ecuación que describe el movimiento entre colisiones para partículas menores que las escalas más pequeñas del flujo (escala de Kolmogorov en flujos turbulentos), dado el campo lejano (promediado) de velocidades es la de Maxey-Riley (MRE). Esta ecuación es el objeto de estudio del capítulo 2. El objetivo de este estudio teórico es establecer de forma cuantitativa (en orden de magnitud) su rango de validez y la importancia relativa de sus distintos términos. El método empleado es el análisis dimensional aplicado sistemáticamente al estudio de los 'primeros efectos' de distintos fenómenos físicos que se desprecian en el planteamiento de la ecuación. El capítulo 3 se centra en la resolución numérica de la MRE. En él se presenta una mejora y estudio sistemático del método de van Hinsberg et al. (2011) para el cálculo del término histórico de la ecuación. Se incluyen distintos tests para demostrar la eficiencia del método y su aplicabilidad práctica. La MRE es de directa aplicación en flujos en los que el número de Reynolds relativo a la partícula es Re << 1. Sin embargo, su relevancia va más allá, pues en su estructura se basan la mayoría de modelos para el movimiento de partículas en suspensión, fuera del rango de aplicación de la MRE. El capítulo 4 es de índole más aplicada que los dos anteriores, y trata diversos ejemplos industriales de flujos con partículas en los que se emplean extensiones de la MRE de este tipo. En la primera parte se revisan las extensiones más importantes y la recuperación de derivadas, proceso necesario para el cálculo de varios términos de la ecuación de movimiento de las partículas. Las aplicaciones prácticas tratadas incluyen el aprisionamiento de burbujas en juntas en 'T', la simulación de sistemas de perforación petrolífera basados en el bombardeo con partículas de acero y los lechos fluidificados. Para esta última, se usa una técnica de filtrado discreto inspirada en la teoría esbozada más arriba. Estos tres capítulos (2, 3, 4) se completan con la introducción (capítulo 1) y las conclusiones (capítulo 5).
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Kwok, Ting On. "Adaptive meshless methods for solving partial differential equations." HKBU Institutional Repository, 2009. http://repository.hkbu.edu.hk/etd_ra/1076.

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Stewart, Dawn L. "Numerical Methods for Accurate Computation of Design Sensitivities." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30561.

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This work is concerned with the development of computational methods for approximating sensitivities of solutions to boundary value problems. We focus on the continuous sensitivity equation method and investigate the application of adaptive meshing and smoothing projection techniques to enhance the basic scheme. The fundamental ideas are first developed for a one dimensional problem and then extended to 2-D flow problems governed by the incompressible Navier-Stokes equations. Numerical experiments are conducted to test the algorithms and to investigate the benefits of adaptivity and smoothing.
Ph. D.
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Bréhier, Charles-Edouard. "Numerical analysis of highly oscillatory Stochastic PDEs." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00824693.

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In a first part, we are interested in the behavior of a system of Stochastic PDEs with two time-scales- more precisely, we focus on the approximation of the slow component thanks to an efficient numerical scheme. We first prove an averaging principle, which states that the slow component converges to the solution of the so-called averaged equation. We then show that a numerical scheme of Euler type provides a good approximation of an unknown coefficient appearing in the averaged equation. Finally, we build and we analyze a discretization scheme based on the previous results, according to the HMM methodology (Heterogeneous Multiscale Method). We precise the orders of convergence with respect to the time-scale parameter and to the parameters of the numerical discretization- we study the convergence in a strong sense - approximation of the trajectories - and in a weak sense - approximation of the laws. In a second part, we study a method for approximating solutions of parabolic PDEs, which combines a semi-lagrangian approach and a Monte-Carlo discretization. We first show in a simplified situation that the variance depends on the discretization steps. We then provide numerical simulations of solutions, in order to show some possible applications of such a method.
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Books on the topic "Particle methods (Numerical analysis)":

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Li, Shaofan. Meshfree particle methods. Berlin: Springer, 2004.

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Liu, G. R. Smoothed particle hydrodynamics: A meshfree particle method. New Jersey: World Scientific, 2003.

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Oñate, Eugenio. Particle-Based Methods: Fundamentals and Applications. Dordrecht: Springer Science+Business Media B.V., 2011.

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International, PFC Symposium (1st 2002 Gelsenkirchen Germany). Numerical modeling in micromechanics via particle methods: Proceedings of the 1st International PFC Symposium, Gelsenkirchen, Germany, 6-8 November 2002. Lisse: Balkema, 2003.

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Ying, Long'an. Numerical methods for exterior problems. Hackensack, NJ: World Scientific, 2006.

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Li, Ronghua. Generalized difference methods for differential equations: Numerical analysis of finite volume methods. New York: M. Dekker, 2000.

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Allgower, E. L. Introduction to numerical continuation methods. Philadelphia: SIAM, 2003.

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1948-, Hackbusch W., Trottenberg U, and European Multigrid Conference (3rd : 1990 : Bonn, Germany), eds. Multigrid methods III. Basel: Birkhäuser Verlag, 1991.

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Hackbusch, W. Multi-grid methods and applications. Berlin: Springer-Verlag, 1985.

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Evans, Gwynne. Numerical methods for partial differential equations. London: Springer, 2000.

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Book chapters on the topic "Particle methods (Numerical analysis)":

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Sibille, Luc, Florent Prunier, François Nicot, and Félix Darve. "Discrete Numerical Analysis of Failure Modes in Granular Materials." In Particle-Based Methods, 187–210. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0735-1_7.

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Williams, Mike. "Numerical Methods and Data Analysis Techniques in Particle Physics." In Springer Proceedings in Physics, 337–58. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12238-0_8.

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Yoshioka, Keita, Mathias Nest, Daniel Pötschke, Amir Shoarian Sattari, Patrick Schmidt, and David Krach. "Numerical Platform." In GeomInt–Mechanical Integrity of Host Rocks, 63–95. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61909-1_3.

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AbstractAn essential scientific goal of the GeomInt project is the analysis of potentials and limitations of different numerical approaches for the modelling of discontinuities in the rocks under consideration in order to improve the understanding of methods and their synergies with regard to theoretical and numerical fundamentals. As numerical methods, the “Lattice Element Method” (LEM), the non-continuous discontinuum methods “Discrete Element Method” (DEM), the “Smoothed Particle Hydrodynamics” (SPH), the “Forces on Fracture Surfaces” (FFS) as well as the continuum approaches “Phase-Field Method” (PFM), “Lower-Interface-Method” (LIE), “Non-Local Deformation” (NLD) and the “Hybrid-Dimensional Finite-Element-Method” (HDF) will be systematically investigated and appropriately extended based on experimental results (Fig. 3.1).
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Meliani, Mohammed Hadj, Hassane Moustabchir, and Zitouni Azari. "T-Stress by Stress Difference Method (SDM): Numerical Analysis on Mode (I) Loading." In Particle and Continuum Aspects of Mesomechanics, 253–60. London, UK: ISTE, 2010. http://dx.doi.org/10.1002/9780470610794.ch25.

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Monforte, Lluís, Marcos Arroyo, Maxat Mamirov, and Jong R. Kim. "Numerical Analysis of Soil Ploughing Using the Particle Finite Element Method." In Springer Series in Geomechanics and Geoengineering, 390–93. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97112-4_87.

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Chaskalovic, Joël. "Applications of Functional Analysis to Partial Differential Equations." In Mathematical and Numerical Methods for Partial Differential Equations, 3–61. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-03563-5_1.

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Giriprasad, A., B. Shruthi, Poonam Upadhyay, and T. Nireekshana. "Analysis on Movement of Conducting Particle by Varying the Particle Dimensions in Gas Insulated Busduct Using Numerical Methods." In Lecture Notes in Electrical Engineering, 595–608. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-8439-8_49.

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Canuto, Claudio, and Marco Verani. "On the Numerical Analysis of Adaptive Spectral/hp Methods for Elliptic Problems." In Analysis and Numerics of Partial Differential Equations, 165–92. Milano: Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2592-9_11.

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Oda, Tsuyoshi, Nobuyuki Satofuka, and Hidetoshi Nishida. "Numerical Analysis of Particle Behavior Penetrating into Liquid by Level Set Method." In Computational Fluid Dynamics 2002, 529–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-59334-5_79.

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Haghighi, Kamyar, and Eun Kang. "A Knowledge-Based Approach to the Adaptive Finite Element Analysis." In Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations, 267–76. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4248-2_14.

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Conference papers on the topic "Particle methods (Numerical analysis)":

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Francomano, Elisa, Adele Tortorici, Elena Toscano, Guido Ala, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Multiscale Particle Method in Solving Partial Differential Equations." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790115.

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Schiller, Annika, Godehard Sutmann, Luis Martinell, Pieter Bellens, Rosa Badia, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Particle Methods on Multicore Architectures: Experiences and Future Plans." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498233.

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Geiser, Jürgen, and Frederik Riedel. "Integrators for particle in cell methods: Comparison and applications." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952245.

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Tofighi, N., A. Zainali, and M. Yildiz. "Modelling of bubble rising by smoothed particle hydrodynamics method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756071.

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Lewtak, Robert, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Numerical Simulation of Particulate Flows using the Multiphase Particle-In-Cell Method." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790147.

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Rowlands, R. E., Z. Feng, and T. D. Dudderar. "Quantitative fluid flow analysis by laser speckle velocimetry and numerical processing." In ICALEO® ‘89: Proceedings of the Optical Methods in Flow & Particle Diagnostics Conference. Laser Institute of America, 1989. http://dx.doi.org/10.2351/1.5058304.

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Darabi, Jeff. "Numerical Analysis of Dielectrophoretic-Based DNA Separation and Trapping." In ASME 2022 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/fedsm2022-87076.

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Abstract In this study, dielectrophoresis (DEP) has been coupled with field-flow fractionation (FFF) for the sorting and trapping of the biological particles. A numerical simulation is performed to compute particle trajectories under the influence of DEP, drag, gravitational, and buoyancy forces, as well as Brownian motion. The simulation was performed using OpenFOAM CFD software. Both positive and negative DEP methods are examined as possible separation techniques for DNA fragments. Positive DEP forces are used to attract the particles to the electrodes and trap them in groups of similar particles while a combination of negative DEP forces and field flow fractionation (FFF) are used to levitate the particles within the fluid flow to certain flow trajectories. The results obtained from this study, including electric field simulations, particle trajectories, elution times, and trapping lengths are presented.
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Shibata, K., S. Koshizuka, and Y. Oka. "Numerical Analysis of Droplet Size Distribution Using Particle Method." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45165.

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A continuous jet changes to droplets where jet breakup occurs. In this study, two-dimensional numerical analysis of jet breakup is performed using MPS method (Moving Particle Semi-implicit Method) which is a particle method for incompressible flows. The continuous fluid surrounding the jet is neglected. The size distribution of droplets is in agreement with the Nukiyama-Tanasawa distribution which has been widely used as an experimental correlation. Effects of the Weber number and the Froude number on the size distribution are also obtained from the calculation.
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Asaoka, Tatsunori, Masashi Okada, Yoshikazu Teraoka, and Akihiro Tsumura. "Numerical Analysis of Natural Convection of Suspension With Particle Sedimentation." In 2010 14th International Heat Transfer Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/ihtc14-22141.

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A new method for the numerical analysis of natural convection of suspension was proposed. Natural convection phenomena of suspension appear in some industrial fields, such as water disposal process and food engineering process. It is difficult to comprehend the behavior of the natural convection of the suspensions, because the convection of the suspension is caused by the interactive effects of the temperature distribution and particle-concentration distribution in the suspension. In this study, a numerical model for the natural convection phenomena of the suspension accompanied by particle sedimentation was constructed. In this model, since the limited number of particles is tracked individually, the movement of each particle which has varied sizes can be achieved. Then the effect of distribution of particle size on the particle-concentration in the suspension can be considered. As a result, it was confirmed that the typical behavior of the natural convection of suspension can be expressed by using this model. Additionally, it was found that the mean Nusselt number of the natural convection of the suspension obtained by using this model shows the same tendency as that of the previous experiments.
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Bento, David, Diana Pinho, Ana I. Pereira, and Rui Lima. "Genetic algorithm and particle swarm optimization combined with Powell method." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825557.

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Reports on the topic "Particle methods (Numerical analysis)":

1

Sparks, Paul, Jesse Sherburn, William Heard, and Brett Williams. Penetration modeling of ultra‐high performance concrete using multiscale meshfree methods. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/41963.

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Terminal ballistics of concrete is of extreme importance to the military and civil communities. Over the past few decades, ultra‐high performance concrete (UHPC) has been developed for various applications in the design of protective structures because UHPC has an enhanced ballistic resistance over conventional strength concrete. Developing predictive numerical models of UHPC subjected to penetration is critical in understanding the material's enhanced performance. This study employs the advanced fundamental concrete (AFC) model, and it runs inside the reproducing kernel particle method (RKPM)‐based code known as the nonlinear meshfree analysis program (NMAP). NMAP is advantageous for modeling impact and penetration problems that exhibit extreme deformation and material fragmentation. A comprehensive experimental study was conducted to characterize the UHPC. The investigation consisted of fracture toughness testing, the utilization of nondestructive microcomputed tomography analysis, and projectile penetration shots on the UHPC targets. To improve the accuracy of the model, a new scaled damage evolution law (SDEL) is employed within the microcrack informed damage model. During the homogenized macroscopic calculation, the corresponding microscopic cell needs to be dimensionally equivalent to the mesh dimension when the partial differential equation becomes ill posed and strain softening ensues. Results of numerical investigations will be compared with results of penetration experiments.
2

Zheng, Jinhui, Matteo Ciantia, and Jonathan Knappett. On the efficiency of coupled discrete-continuum modelling analyses of cemented materials. University of Dundee, December 2021. http://dx.doi.org/10.20933/100001236.

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Computational load of discrete element modelling (DEM) simulations is known to increase with the number of particles. To improve the computational efficiency hybrid methods using continuous elements in the far-field, have been developed to decrease the number of discrete particles required for the model. In the present work, the performance of using such coupling methods is investigated. In particular, the coupled wall method, known as the “wall-zone” method when coupling DEM and the continuum Finite Differences Method (FDM) using the Itasca commercial codes PFC and FLAC respectively, is here analysed. To determine the accuracy and the efficiency of such a coupling approach, 3-point bending tests of cemented materials are simulated numerically. To validate the coupling accuracy first the elastic response of the beam is considered. The advantage of employing such a coupling method is then investigated by loading the beam until failure. Finally, comparing the results between DEM, DEM-FDM coupled and FDM models, the advantages and disadvantages of each method are outlined.
3

Rozovskii, Boris, and Alexander Tartakovsky. Nonlinear Filtering: Analysis and Numerical Methods. Fort Belvoir, VA: Defense Technical Information Center, November 2001. http://dx.doi.org/10.21236/ada399200.

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Flanagan, R. D., M. A. Tenbus, and R. M. Bennett. Numerical methods for analysis of clay tile infills. Office of Scientific and Technical Information (OSTI), October 1993. http://dx.doi.org/10.2172/10186487.

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Clayton, John D., Peter W. Chung, Michael A. Greenfield, and WIlliam D. Nothwang. Numerical Methods for Analysis of Charged Vacancy Diffusion in Dielectric Solids. Fort Belvoir, VA: Defense Technical Information Center, December 2006. http://dx.doi.org/10.21236/ada459751.

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Page, William, Brian Fisk, and William Zimmerman. Development of Numerical Simulation Methods for Analysis of Laser Guided Arc Discharge. Fort Belvoir, VA: Defense Technical Information Center, February 2008. http://dx.doi.org/10.21236/ada483004.

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Eisenberg, Michael. Descriptive Simulation: Combining Symbolic and Numerical Methods in the Analysis of Chemical Reaction Mechanisms. Fort Belvoir, VA: Defense Technical Information Center, September 1989. http://dx.doi.org/10.21236/ada214678.

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Citerley, Richard L., and Narendra S. Khot. Numerical Methods for Imperfection Sensitivity Analysis of Stiffened Cylindrical Shells. Volume 1. Development and Applications. Fort Belvoir, VA: Defense Technical Information Center, September 1986. http://dx.doi.org/10.21236/ada179686.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada244273.

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Chan, Tony F. Numerical Methods for Solving Large Sparse Eigenvalue Problems and for the Analysis of Bifurcation Phenomena. Fort Belvoir, VA: Defense Technical Information Center, October 1991. http://dx.doi.org/10.21236/ada246470.

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