A review of numerical asymptotic averaging for weakly nonlinear hyperbolic waves

We present an overview of averaging method for solving weakly nonlinear hyperbolic systems. An asymptotic solution is constructed, which is uniformly valid in the “large” domain of variables t + |x| ∼ O(ϵ –1). Using this method we obtain the averaged system, which disintegrates into independent equations for the nonresonant systems. A scheme for theoretical justification of such algorithms is given and examples are presented. The averaged systems with periodic solutions are investigated for the following problems of mathematical physics: shallow water waves, gas dynamics and elastic waves. In the resonant case the averaged systems must be solved numerically. They are approximated by the finite difference schemes and the results of numerical experiments are presented. Silpnai netiesinių hiperbolinių sistemų skaitinio asimptotinio vidurkinimo apžvalga Santrauka Darbe nagrinėjamas silpnai netiesinių hiperbolinių sistemų ilgųjų bangų asimptotinis sprendinys. Siūlomas jo konstravimo metodas, pagrįstas vidurkinimu bei dviejų mastelių principu. Užrašytos skirtuminės schemos suvidurkintų lygčių sistemoms spręsti. Ištirti trys periodinių asimptotinių sprendinių pavyzdžiai: sekliųjų vandenų modelis, dujų dinamikos lygtys bei tampriųjų bangų sąveika. First Published Online: 14 Oct 201

Modeling and simulations of beam stabilization in edge-emitting broad area semiconductor devices

A 2+1 dimensional PDE traveling wave model describing spatial-lateral dynamics of edge-emitting broad area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is presented and implemented on a parallel compute cluster. Simulations of the model equations are used for optimizing of existing devices with respect to the emitted beam quality, as well as for creating and testing of novel device design concept

Analysis of upwind and high‐resolution schemes for solving convection dominated problems in porous media

The conservation laws governing the multiphase flows in porous media are often convection‐dominated and have a steep fronts that require accurate resolution. Standard discretization methods of the convection terms do not perform well for such problems. The main aim of this work is to analyze the use of upwind and high‐ resolution schemes in such cases. First, we use a first differential approximation method to perform a theoretical analysis of a standard upwind approximation and different time stepping schemes for the linear hyperbolic equations in 1‐ and 2D. Next, we present a popular approach to reduce the amount of numerical diffusion introduced by upwind approximation ‐ high‐resolution schemes. We compare our implementation of one of the recently proposed central‐upwind schemes against the upwind schemes on several test problems based on Buckley‐Leverett equation and discuss the results. Finally, a parallel version of central‐upwind scheme in 2D is presented. It was implemented using our C++ library of parallel arrays ‐ ParSol. First Published Online: 14 Oct 201

Parallel numerical modelling of short laser pulse compression

In this paper we investigate parallel numerical algorithms for solution of the transient stimulated scattering processes. A new symmetrical splitting scheme is proposed and a parallel version is given. The efficiency of the parallel algorithm is investigated for two cases. The first one describes a case when the computation region is constant during the whole time of computations. The second one describes the initial phase of the process, when the computational region increases linearly in time. In order to distribute more evenly jobs between processors a dynamical the grid redistribution algorithm is is used. We also give a proof of one result about optimal static grid distribution in the case of linearly increased problem complexity. The results of computations are presented. They were obtained on different parallel computers and clusters of workstations. Trumpų lazerio impilsų spūdos skaičiavimo lygiagretusis skaitinis algoritmas Santrauka Nagrinejamas priverstines Brijueno sklaidos fokusuotuose pluoštuose uždavinio lygiagretusis skaitinis sprendimo algoritmas. Sukonstruota simetrinio skaidymo baigtiniu skirtumu schema, kurios tikslumas yra antrosios eiles. Lygiagretusis algoritmas gautas naudojant duomenu lygiagretumo paradigma. Detaliai nagrinejamas dinamiškai didejančio sudetingumo uždavinys, modeliuojantis Brijueno sklaidos procesa, kai neužduodama kraštine salyga Stokso bangai. Irodyta hipoteze apie vieno stacionaraus blokinio duomenu paskirstymo algoritmo op‐timaluma. Eksperimentiškai ištirtas dinaminis duomenu perskirstymo algoritmas, patvirtintas jo efektyvumas net ir fiksuoto dydžio uždaviniams. Darbe pateikti skaitinio eksperimento, atlikto naudojant VGTU 20 procesoriu klasteri, rezultatai. Jie patvirtino gautuosius teorinius rezultatus, išsam us fizikiniai rezultatai bus išspausdinti kituose darbuose. First Published Online: 14 Oct 201

A parallel algorithm for solving one problem of nonlinear optics

This paper deals with a system of nonlinear differential equations, which describe the interaction of two focused laser beams in nonlinear media. The system of equations is approximated by a splitting finite difference scheme. A parallel version of the finite‐difference scheme is proposed and the efficiency of this algorithm is investigated. Calculations are performed using clusters of computers, connected via local computer network. The emphasis is made on solving this problem on heterogeneous clusters. In the paper a static distribution scheme is analyzed. The results of several computational experiments are presented. Data redistribution during an initial phase of computation is investigated and the influence of slow communication among the processes is taken into account during this analysis. Netiesinės optikos uždavinio lygiagretusis skaičiavimo algoritmas Santrauka Straipsnyje sprendžiama netiesiniu diferencialiniu lygčiu sistema, aprašanti lazerio spinduliu saveika netiesineje terpeje. Sudaryta diskrečioji išskaidymo schema bei pateikta lygiagrečioji algoritmo versija. Ištirtas lygiagrečiojo algoritmo efektyvumas. Skaičiavimai atlikti virtualiajame kompiuteriu, sujungtu lokaliuoju tinklu, klasteryje. Išsamiai tiriamas algoritmo efektyvumas heterogeniniams lygiagretiesiems kompiuteriams. Duomenu paskirstymui naudojamas statinis paskirstymo metodas. Pateikti ir išanalizuoti duomenu perskirstymo algoritmai, pagerinantys darbo paskirstymo tolyguma pradineje skaičiavimu fazeje. Teorineje analizeje atsižvelgiama i duomenu perdavimo kaštus. First Published Online: 14 Oct 201

Parallel algorithms for solution of nonlinear diffusion problems in image smoothing

In this work we consider parallel algorithms for solution of nonlinear parabolic PDEs. First mathematical models describing nonlinear diffusion filters are presented. The finite‐volume method is used to approximate differential equations. Parallel algorithms are based on the domain decomposition method. The algorithms are implemented by using ParSol parallelization tool and a brief description of this tool is also presented. The efficiency of proposed parallel algorithms is investigated and results of the scalability analysis are given. Theoretical predictions are compared with results of computational experiments. Application of nonlinear diffusion filters for analysis of computer tomography images is discussed in the last section of the paper. Šiame darbe nagrinejami lygiagretieji algoritmai, kurie skirti netiesiniu nestacionariu difuzijos lygčiu sprendimui. Pirmiausia yra suformuluoti netiesiniu filtru matematiniai modeliai. Šie uždaviniai aproksimuoti baigtiniu tūriu schemomis. Lygiagretieji algoritmai konstruojami duomenu lygiagretumo metodu. Jie realizuoti autoriu sukurtu ParSolprogramavimo irankiu. Pateiktas trumpas šio irankio aprašymas. Ištirtas lygiagrečiuju algoritmu efektyvumas ir pateikti algoritmu išplečiamumo analizes rezultatai. Teorines išvados palygintos su skaičiavimo rezultatais. Netiesiniai difuziniai filtrai pritaikyti galvos kompiuteriniu tomogramu filtravimui. First Published Online: 14 Oct 201

To know or not to know:should crimes regarding photographs of their child sexual abuse be disclosed to now-adult, unknowing victims?

This paper considers the unexplored question of whether unaware crime victims have rights or interests in knowing and not knowing information pertaining to the crime(s) committed against them. Our specific focus is on whether crimes regarding abusive images (AI) should be disclosed to now-adult victims of child sexual abuse who feature in them. Because these issues have not been addressed in the victimology or criminological literature, we utilise literature in another discipline - health care ethics and law - to inform our analysis. Through engaging with the debate on the right to know and not to know information concerning one’s genetic status, we develop a conceptualisation of the issues regarding unknowing AI victims. A rights-based conceptualisation proves to be largely inappropriate; we contend that, instead, it would be more productive to look to unknowing AI victims’ interests. We argue that the interests at stake are grounded in autonomy and/or spatial privacy, and that in order to find a way to resolve the disclosure dilemma, these interests must be considered alongside consequentialist concerns; disclosing information regarding AI could empower now-adult victims but could well cause them (further) harm. Finally, we consider the implications of our analysis for victimology