The traditional Method of Fundamental Solutions is revisited, based on a special strategy of defining the external source points. Unlike the classical Method of Fundamental Solutions, the sources are ...categorized into groups; the density of the spatial distribution of the sources decreases rapidly far from the boundary. On each group, the original problem is discretized using the same set of boundary collocation points. Such groups of sources are constructed in a fully automated way by the quadtree/octtree algorithm. The discretized problems are solved in the sense of least squares. A simple multi-level method is built up, using the (conjugate) gradient iteration as a smoothing procedure. The resulting method significantly reduces the computational complexity. Moreover, the problem of evaluation singular integrals as well as the problem of severely ill-conditioned matrices are avoided. The method is generalized to 3D axisymmetric potential problems as well.
The method of fundamental solutions is investigated in the case when the source points are located along the boundary of the domain of the original problem and coincide with the collocation points. ...The appearing singularities are eliminated by several techniques: by using approximate but continuous fundamental solutions (regularization) and via auxiliary subproblems to avoid the stronger singularities that appear in the normal derivatives of the fundamental solution (desingularization). Both monopole and dipole formulations are investigated. A special iterative solution algorithm is presented, which converts the original (mixed) problem to a sequence of pure Dirichlet and pure Neumann subproblems. The pure subproblems can be handled efficiently by using conjugate gradients. The efficiency is significantly increased by embedding the resulting method in a natural multi-level context. At the same time, the problem of the use of highly ill-conditioned matrices is also avoided.
A novel meshless method is presented. It is based on completing the original problem with an additional one which is defined in the same domain and connected with the original problem through the ...boundary only. The boundary conditions are enforced by some internal sources appearing in the supplementary problem only. The fundamental solutions are not used explicitly. The two problems are solved simultaneously using computationally quite efficient multi-level tools. No dense and ill-conditioned linear systems have to be solved. Moreover, no external or boundary sources are to be located. The approach can easily be extended to more general elliptic problems in a natural way, since the corresponding fundamental solution is not needed to be known.
Both artificial and natural regeneration of oaks strongly depend on the quantity and quality of the acorn crop, which show high year-to-year variation. The volume of the acorn crop is influenced by ...many factors including biotic and abiotic effects. The quality (i.e., germination ability, nutrient reserves) of acorns can be decreased by carpophagous insect and fungal pathogen damage or by inadequate weather conditions. Defoliating insects (caterpillars, sawfly larva, etc.) can significantly decrease the acorn crop as well. The most important predators of the defoliators are insectivorous birds during their nesting period. However, in the oak forests of the northern Hungarian mountains, there is a shortage of natural nesting holes. The main aim of our study was to artificially increase the number of the available nesting holes by nest boxes and to maximize the number of breeding insectivorous birds and register the direct (Lepidoptera densities) and indirect (acorn crop quantity and quality) effects of their presence. We found only slight effects on Lepidoptera densities, so we failed to demonstrate a direct effect in the relatively low time frame of our study. But, we could show the indirect positive effect of increased predation on the health state of the acorn crop, resulting in higher seedling densities, which may improve the natural regeneration potential of sessile oak. This result supports the outstanding importance of natural nesting holes in broadleaved forests.
The North American oak lace bug (OLB,
) was first found in Europe in northern Italy in 2000, and up to 2019 it was recorded in 20 countries. Almost all Eurasian deciduous oak species are suitable ...hosts and the species can also feed on many other woody plants. At least 30 million hectares of oak forests provide suitable hosts for the OLB, meaning that the lack of suitable hosts will not restrict its further spread. Detailed studies on the long-term impact of the species are not yet available but there are many good reasons to assume that it poses multiple threats to oaks and oak ecosystems. In the long term, it may have negative effects on oak health, growth, and acorn crops. Many of other oak-associated species will likely also be negatively affected. So far, no effective and environmentally tolerable large scale control method is known for OLB.
Abstract A localized version of the Method of Fundamental Solutions is applied to the 2D steady heat transfer equation with spatially varying thermal conductivity. Though the corresponding ...fundamental solution cannot be computed in general, the localization splits the original problem into several subproblems defined on small subdomains; in these subdomains, the subproblems are approximately converted to certain convection-diffusion equations with constant coefficients, so that the Method of Fundamental Solutions is applicable. In each subdomain, the corresponding subproblem is solved separately. This results in an iterative method, which mimics the overlapping (alternating) Schwarz method. Due to its advantageous numerical properties, the technique seems a useful generalization of the Method of Fundamental Solutions. The method is illustrated through numerical examples.
The method of fundamental solutions and some versions applied to mixed boundary value problems are considered. Several strategies are outlined to avoid the problems due to the singularity of the ...fundamental solutions: the use of higher order fundamental solutions, and the use of nearly fundamental solutions and special fundamental solutions concentrated on lines instead of points. The errors of the approximations as well as the problem of ill-conditioned matrices are illustrated via numerical examples.
Numerous recent studies report an alarming decrease in diversity, biomass, or abundance of arthropods in various habitats. Given that they are important food for other organisms, the ecological ...consequences of such a decline could be severe. We used data from the Hungarian Forestry Light Trap Network to examine whether the spring caterpillar biomass showed any long term (23–58 years) declining trend in oak-dominated forests. Light trap data for 43 selected macrolepidopteran species (suitable bird food in the larval stage) from six different locations were used for the estimation of the total available caterpillar biomass. Time series analyses showed strong year-to-year fluctuations, and over all locations and time windows there was an increasing rather than decreasing trend. The increase found at some locations may suggest increasing herbivore pressure and negative impacts on forest health. We conclude that foliage-feeding macrolepidopteran species with spring-developing larvae did not show a drastic decrease in recent decades, and food availability in the long term will not negatively influence the breeding success of birds in such forests.
Interests in the use of chemometric and data science methods for laboratory techniques have grown rapidly over the last 10 years, for the reason that they are cheaper and faster than traditional ...analytical methods of material testing. This study uses 888 rock samples collected from the exploration and production (E&P) sector of the oil industry. Based on the Fourier‐transform infrared (FT‐IR) spectra of these rock samples their solubility predictions have been developed and investigated with nine methods including both linear and non‐linear ones. Two of these methods such as Partial Least Squares Regression (PLSR) and Support Vector Regression (SVR) are available in a commercial software package and the other seven methods, Extreme Gradient Boosting (XGBoost), Ridge Regression (RR), k‐nearest neighbours (k‐NN), Decision Tree (DT), Multilayer Perceptron (MLP), Support Vector Regression (SVR), Artificial Neural Network (ANN) with TensorFlow (TF), were coded by the authors based either on commercial applications or open source libraries. The investigation starts with spectral data pre‐processing carried out by standard normal variate (SNV), baseline correction and feature selection methods creating the feature set for all machine learning (ML) applications. The accuracy of predictions has been evaluated with mean squared error as a performance metric for each investigated method. The comparisons of predicted values to real data of test samples have shown that mineral solubility in acids can be well predicted in the range of the uncertainties of real laboratory measurements, therefore it can be used to improve the response time of these investigations and reduce the risk in industrial applications. In those cases, where the unknown samples have got some out of the range features, the limitations in the accuracy of predictions have become clear. We have also identified the limitations in the methodology and planned steps to further improve the prediction capabilities. The identified constraint of samples' multitude further emphasizes the need for database building efforts, so that the real potential in big data and machine learning can be realized.
Rock samples were collected from the E&P sector of the oil industry. Based on the FT‐IR spectra of the rock samples their solubility predictions have been developed and investigated. The comparisons of predicted values to real data of test samples have shown that mineral solubility in acids can be well predicted in the range of the uncertainties of real laboratory measurements, therefore it can be used to improve the response time of these investigations and reduce the risk in industrial applications.
Abstract The North American oak lace bug ( Corythucha arcuata ) was first discovered in Europe (Norhern Italy) in 2000. It started a rapid area expansion in the last decade and has been reported in ...20 countries so far. Almost all European oaks are suitable hosts. On top of the host availability, abiotic factors like weather/climate may also have a decisive impact on its further spread and future outbreaks. We conducted a simple field survey within three years, at five locations to estimate the overwintering mortality of the species. Our results suggest that not even a relatively harsh winter (as 2016/2017) caused severe mortality in the overwintering populations. The average mortality of the nine year/location combinations was 30.6% (range 9.1–58.5%). Based on this, the low winter temperature is unlikely to restrict its further spread, therefore continuing area expansion can be predicted.
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