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Visualisation of the electromagnetic vector fields 可视化的电磁矢量场
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.01
S. Barton
{"title":"Visualisation of the electromagnetic vector fields","authors":"S. Barton","doi":"10.21136/panm.2022.01","DOIUrl":"https://doi.org/10.21136/panm.2022.01","url":null,"abstract":"Modern computer algebra software can be used to visualize vector fields. One of the most used is the Maple program. This program is used to visualize two and three-dimensional vector fields. The possibilities of plotting direction vectors, lines of force, equipotential curves and the method of colouring the surface area for two-dimensional cases are shown step by step. For three-dimensional arrays, these methods are applied to various slices of three-dimensional space, such as a plane or a cylindrical surface. Finally, the temporal evolution of the vector fields is illustrated by animations based on the above methods. In contrast to the publication [2], which deals only with the problem of colouring vector fields, the present paper makes a completely comprehensive study of the problem, including the representation of vectors in a predefined network, the computation of the shape of power lines, and the animation of time changes, including the animation of the coloured vector fields.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126215367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finding vertex-disjoint cycle cover of undirected graph using the least-squares method 用最小二乘法求无向图的顶点不相交环盖
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.10
J. Lamač, M. Vlasák
{"title":"Finding vertex-disjoint cycle cover of undirected graph using the least-squares method","authors":"J. Lamač, M. Vlasák","doi":"10.21136/panm.2022.10","DOIUrl":"https://doi.org/10.21136/panm.2022.10","url":null,"abstract":"We investigate the properties of the least-squares solution of the system of equations with a matrix being the incidence matrix of a given undirected connected graph $G$ and we propose an algorithm that uses this solution for finding a vertex-disjoint cycle cover (2-factor) of the graph $G$.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123704806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters 具有不确定材料参数的达西流动随机Galerkin公式的约基求解器
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.02
M. Béres
{"title":"Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters","authors":"M. Béres","doi":"10.21136/panm.2022.02","DOIUrl":"https://doi.org/10.21136/panm.2022.02","url":null,"abstract":"In this contribution, we present a solution to the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material coefficients in the separable form. The SG system of equations is kept in the compressed tensor form and its solution is a very challenging task. Here, we present the reduced basis (RB) method as a solver which looks for a low-rank representation of the solution. The construction of the RB consists of iterative expanding of the basis using Monte Carlo sampling. We discuss the setting of the sampling procedure and an efficient solution of multiple similar systems emerging during the sampling procedure using deflation. We conclude with a demonstration of the use of SG solution for forward uncertainty quantification.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"161 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129104130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The impact of uncertain parameters on ratchetting trends in hypoplasticity 不确定参数对低塑性棘轮趋势的影响
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.04
J. Chleboun, J. Runcziková, Pavel Krejčí
{"title":"The impact of uncertain parameters on ratchetting trends in hypoplasticity","authors":"J. Chleboun, J. Runcziková, Pavel Krejčí","doi":"10.21136/panm.2022.04","DOIUrl":"https://doi.org/10.21136/panm.2022.04","url":null,"abstract":"Perturbed parameters are considered in a hypoplastic model of granular materials. For fixed parameters, the model response to a periodic stress loading and unloading converges to a limit state of strain. The focus of this contribution is the assessment of the change in the limit strain caused by varying model parameters.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127640610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Wildfires identification: Semantic segmentation using support vector machine classifier 野火识别:基于支持向量机分类器的语义分割
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.16
Marek Pecha, Zachary L. Langford, D. Hořák, Richard Tran Mills
{"title":"Wildfires identification: Semantic segmentation using support vector machine classifier","authors":"Marek Pecha, Zachary L. Langford, D. Hořák, Richard Tran Mills","doi":"10.21136/panm.2022.16","DOIUrl":"https://doi.org/10.21136/panm.2022.16","url":null,"abstract":"This paper deals with wildfire identification in the Alaska regions as a semantic segmentation task using support vector machine classifiers. Instead of colour information represented by means of BGR channels, we proceed with a normalized reflectance over 152 days so that such time series is assigned to each pixel. We compare models associated with $mathcal{l}1$-loss and $mathcal{l}2$-loss functions and stopping criteria based on a projected gradient and duality gap in the presented benchmarks.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125481872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interpolation with restrictions -- role of the boundary conditions and individual restrictions 有限制的插值——边界条件和个别限制的作用
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.26
J. Valášek, P. Sváček
{"title":"Interpolation with restrictions -- role of the boundary conditions and individual restrictions","authors":"J. Valášek, P. Sváček","doi":"10.21136/panm.2022.26","DOIUrl":"https://doi.org/10.21136/panm.2022.26","url":null,"abstract":"The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another is a dissipative method not respecting conservation laws, a conservative interpolation method introducing constraints is described. The constraints have form of Lagrange multipliers enforcing conservation of desired flow quantities, like e.g. total fluid mass, flow kinetic energy or flow potential energy. Then the interpolation problem turns into an error minimization problem, such that the resulting quantities of proposed interpolation satisfy these physical properties while staying as close as possible to the results of Lagrangian interpolation in the L2 norm. The proposed interpolation scheme does not impose any restrictions on mesh generation process and it has a relatively low computational cost. The implementation details are discussed and test cases are shown.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130349687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
DGM for real options valuation: Options to change operating scale DGM用于实物期权估值:改变经营规模的期权
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.08
J. Hozman, T. Tichý
{"title":"DGM for real options valuation: Options to change operating scale","authors":"J. Hozman, T. Tichý","doi":"10.21136/panm.2022.08","DOIUrl":"https://doi.org/10.21136/panm.2022.08","url":null,"abstract":"The real options approach interprets a flexibility value, embedded in a project, as an option premium. The object of interest is to valuate real options to change operating scale, typical for natural resources industry. The evolution of the project as well as option prices is decribed by partial differential equations of the Black-Scholes type, linked through a payoff function given by a type of the flexibility provided. The governing equations are discretized by the discontinuous Galerkin method over a finite element mesh and they are integrated in temporal variable by an implicit Euler scheme. The special attention is paid to the treatment of early exercise feature that is handled by additional penalty term. The capabilities of the approach presented are documented on the selected individual real options from the reference experiments using real market data.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115754933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Residual norm behavior for Hybrid LSQR regularization 混合LSQR正则化残差范数行为
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.07
E. Havelková, I. Hnětynková
{"title":"Residual norm behavior for Hybrid LSQR regularization","authors":"E. Havelková, I. Hnětynková","doi":"10.21136/panm.2022.07","DOIUrl":"https://doi.org/10.21136/panm.2022.07","url":null,"abstract":"Hybrid LSQR represents a powerful method for regularization of large-scale discrete inverse problems, where ill-conditioning of the model matrix and ill-posedness of the problem make the solutions seriously sensitive to the unknown noise in the data. Hybrid LSQR combines the iterative Golub-Kahan bidiagonalization with the Tikhonov regularization of the projected problem. While the behavior of the residual norm for the pure LSQR is well understood and can be used to construct a stopping criterion, this is not the case for the hybrid method. Here we analyze the behavior of norms of approximate solutions and the corresponding residuals in Hybrid LSQR with respect to the Tikhonov regularization parameter. This helps to understand convergence properties of the hybrid approach. Numerical experiments demonstrate the results in finite precision arithmetic.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114119458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Numerical optimization of parameters in systems of differential equations 微分方程系统参数的数值优化
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.12
Josef Martínek, V. Kučera
{"title":"Numerical optimization of parameters in systems of differential equations","authors":"Josef Martínek, V. Kučera","doi":"10.21136/panm.2022.12","DOIUrl":"https://doi.org/10.21136/panm.2022.12","url":null,"abstract":"We present results on the estimation of unknown parameters in systems of ordinary differential equations in order to fit the output of models to real data. The numerical method is based on the nonlinear least squares problem along with the solution of sensitivity equations corresponding to the differential equations. We will present the performance of the method on the problem of fitting the output of basic compartmental epidemic models to data from the Covid-19 epidemic. This allows us to draw several conclusions on the natural limitations of these models and their validity.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"33 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123006796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Determination of the initial stress tensor from deformation of underground opening -- theoretical background and applications 地下巷道变形初始应力张量的确定——理论背景与应用
Programs and Algorithms of Numerical Mathematics 21 Pub Date : 2023-04-24 DOI: 10.21136/panm.2022.11
J. Maĺık, A. Kolcun
{"title":"Determination of the initial stress tensor from deformation of underground opening -- theoretical background and applications","authors":"J. Maĺık, A. Kolcun","doi":"10.21136/panm.2022.11","DOIUrl":"https://doi.org/10.21136/panm.2022.11","url":null,"abstract":"In this paper a method for the detection of initial stress tensor is proposed. The method is based on measuring distances between some pairs of points located on the wall of underground opening in the excavation process. This methods is based on the solution of eighteen auxiliary problems in the theory of elasticity with force boundary conditions. The optimal location of the pairs of points on the wall of underground work is studied. The pairs must be located so that the condition number of a certain matrix has the minimal value, which guarantees a reliable estimation of initial stress tensor.","PeriodicalId":197168,"journal":{"name":"Programs and Algorithms of Numerical Mathematics 21","volume":"35 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133622530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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