Boundary element method application to numerical solving of linear boundary-value problems in domains with strongly segmented boundary

В настоящей работе метод граничных элементов был применен к решению краевых задач для уравнения Лапласа в плоской области с сильно сегментированной границей. Особое внимание было уделено точности численного решения, которая исследовалась путем численного эксперимента на специально подобранных тестовых задачах, имеющих аналитические решения в квадратурах. Было реализовано два алгоритма метода граничных элементов: традиционный с решением системы линейных алгебраических уравнений методами гауссовского исключения, и итерационный, при этом в итерационном алгоритме использовались функции Грина или их вычислительные аналоги. Результаты работы могут быть использованы при создании специализированного программного обеспечения соответствующего назначения.One of the most serious problems of modern numerical analysis is boundary-value problem solution in domains of complex geometrical shapes. Such problems are proved especially difficult for the domains with strongly segmented boundary, which meansthat the boundary is divided into isolated pieces. Such situations are specific for heterogeneous media. In such situations local approximation methods have to deal with the insuperable difficulties such as constructing computational grid and subsequent solving rather sophisticated systems of linear algebraic equations. The methods of global approximations and, first of all, methods of computational potential theory do not have similar difficulties, nevertheless they have to overcome a lot of problems. Boundary element method is applied in thepresent work to solve boundary-value problems for Laplace equations in plane domain with strongly segmented boundary. Special attention in the work was paid to accuracy of numerical solutions. The accuracy is investigated by a numerical experiment using specially selected test problems, which have the known analytical solutions in quadrature. Two boundary element algorithms are implemented. The first one is the traditional approach with Gauss elimination algorithm for solving linear algebraic equation system. The second one is an iterative approach with possible using of Green’s functions or their computational analogs in the iterative procedure. The results obtained in the work can be applied for creating specialized software of corresponding purposes

The ecology of algal assemblages across a gradient of acid mine drainage stress on the West Coast, South Island, New Zealand

Physicochemical factors, algal diversity, taxonomic composition and standing crop were investigated across a broad gradient of AMD stress in streams and rivers. 52 sites were surveyed in the vicinity of Greymouth, Reefton, Westport and Blackball, on the West Coast, South Island. Seven sites in the Reefton area were sampled from April 2006 - February 2007 to establish changes over time in benthic algal communities of AMD and reference streams. Longitudinal change and ecosystem recovery were also investigated by sampling eight sites down Devils Creek, Reefton, and two of its tributaries. AMD has negative impacts on algal diversity, generally increases the dominance of certain taxa and, where metal oxide deposition or hydraulic disturbance are not great, can lead to algal proliferations. These proliferations were chlorophyte dominated, predominantly by filamentous Klebsormidium acidophilum. From the general survey a total of 15 taxa were identified from the most severely impacted sites (pH <3.6), which included both acidophiles and acidotolerant algae. Multivariate analyses strongly suggest that pH was the dominant factor controlling taxonomic occurrence of diatoms, macroalgae and the structure of the total assemblage. Other factors such as conductivity, metal oxide deposition, temperature, depth, month, geographic location and altitude were also important. Algal communities changed over time and this became more marked as AMD impact decreased. This was presumably due to AMD stressors reducing diversity, and thus the available scope for assemblage change. Longitudinal differences in assemblage structure within Devils Creek appeared to be in response to dilution of AMD in upper reaches and to changes in natural physical features such as gradient in mid and lower reaches. After a distance of 7.2 km the physicochemical effects of AMD and suspended clay inputs were minimal. At this site and at several previous sites, the assemblage exhibited a degree of recovery towards that found at unimpacted sites. A range of algae found in the broad scale-survey are potentially useful 'sensitive' indicators. These included: Heteroleibleinia purpurascens; Achnanthes oblongella; Oedogonium sp. and Spirogyra sp. In contrast: Euglena mutabilis; Navicula cincta; K. acidophilum; Microspora quadrata and Microthamnion kuetzingianum may be useful 'tolerance' indicators. These data show that AMD has a range of negative impacts on algae, and algae may be a useful tool for monitoring these impacts in West Coast streams

Orientation dependence of thermal and mechanical hysteresis in Ni51Fe18Ga27Co4 single crystals

The orientation dependence of thermal ΔТ and mechanical Δσ hysteresis was investigated in Ni51Fe18Ga27Co4 single crystals as-grown with isobaric (shape memory effect) and isothermal (superelasticity) experiments. Single crystals oriented along the [001]-direction show a high reversible deformation of 001 ЭПФ ε = (4,0 ± 0,2) % for martensitic transformations, small thermal hysteresis ΔТ = (22 ± 2) K and mechanical Δσ001 = (47 ± 2) МПа hysteresis, as compared with to single crystals oriented along the [110]-direction. Such orientation dependence is determined by the contribution of the L10-martensite under the εdetw in deformation of transformation