In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.
{"title":"Fast multigrid solver","authors":"P. Vanek","doi":"10.21136/am.1995.134274","DOIUrl":"https://doi.org/10.21136/am.1995.134274","url":null,"abstract":"In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"112 1","pages":"1-20"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77920844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper deals with a theoretical model of the Crowel-Alipanahi correlator. The model describes a new possible effect of the DLTS spectra-exponential and nonexponential transient capacitance, normal or anomalous spectra.
{"title":"Functional equations and a theoretical model of DLTS","authors":"V. Tryhuk","doi":"10.21136/am.1995.134308","DOIUrl":"https://doi.org/10.21136/am.1995.134308","url":null,"abstract":"The paper deals with a theoretical model of the Crowel-Alipanahi correlator. The model describes a new possible effect of the DLTS spectra-exponential and nonexponential transient capacitance, normal or anomalous spectra.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"27 1","pages":"473-482"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87309377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
During the last years the interest in the numerical simulation of reacting flows has grown considerably. Numerical methods are available, which allow to couple chemical kinetics with flow and molecular transport. However, the use of detailed physical and chemical models, involving more than 100 chemical species, and thus more than 100 species conservation equations, is restricted to very simple flow configurations like one-dimensional systems or two-dimensional systems with very simple geometries, and models are required, which simplify chemistry without sacrificing accuracy. In many chemically reacting flows chemical processes occur with time scales differing by many orders of magnitude (e.g., 10$^{-10}$ s to 1 s in combustion processes), whereas the time scales of flow, molecular transport, and turbulence usually cover a much smaller range of time scales. Based on local time scale analyses it is possible to decouple the fast (and thus not rate limiting) chemical processes. In this way the chemistry can be described in terms of a small number of governing reaction progress variables, and computations of complex reacting flow problems become possible. Examples for calculations with detailed and simplified chemistry are shown for various reacting flows, such as hypersonic reacting flows or combustion processes.
{"title":"Coupling of chemical reaction with flow and molecular transport","authors":"U. Maas","doi":"10.21136/am.1995.134293","DOIUrl":"https://doi.org/10.21136/am.1995.134293","url":null,"abstract":"During the last years the interest in the numerical simulation of reacting flows has grown considerably. Numerical methods are available, which allow to couple chemical kinetics with flow and molecular transport. However, the use of detailed physical and chemical models, involving more than 100 chemical species, and thus more than 100 species conservation equations, is restricted to very simple flow configurations like one-dimensional systems or two-dimensional systems with very simple geometries, and models are required, which simplify chemistry without sacrificing accuracy. In many chemically reacting flows chemical processes occur with time scales differing by many orders of magnitude (e.g., 10$^{-10}$ s to 1 s in combustion processes), whereas the time scales of flow, molecular transport, and turbulence usually cover a much smaller range of time scales. Based on local time scale analyses it is possible to decouple the fast (and thus not rate limiting) chemical processes. In this way the chemistry can be described in terms of a small number of governing reaction progress variables, and computations of complex reacting flow problems become possible. Examples for calculations with detailed and simplified chemistry are shown for various reacting flows, such as hypersonic reacting flows or combustion processes.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"57 1","pages":"249-266"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75453041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a posteriori error estimators which can be derived by a defect correction in higher order ansatz spaces or by taking advantage of superconvergence results. The performance of the algorithms is illustrated by several numerical examples.
{"title":"Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods","authors":"R. Hoppe, B. Wohlmuth","doi":"10.21136/AM.1995.134292","DOIUrl":"https://doi.org/10.21136/AM.1995.134292","url":null,"abstract":"We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a posteriori error estimators which can be derived by a defect correction in higher order ansatz spaces or by taking advantage of superconvergence results. The performance of the algorithms is illustrated by several numerical examples.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"115 1","pages":"227-248"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79042957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Statistical applications of order $alpha $-$beta $ weighted information energy","authors":"M. Pardo, J. A. Pardo","doi":"10.21136/am.1995.134296","DOIUrl":"https://doi.org/10.21136/am.1995.134296","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"25 1","pages":"305-317"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73197720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Shape optimization of elastic axisymmetric plate on an elastic foundation","authors":"Petr Salač","doi":"10.21136/am.1995.134297","DOIUrl":"https://doi.org/10.21136/am.1995.134297","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"41 1","pages":"319-338"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77643340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary. A general class of numerical methods for solving initia l va l ue prob l ems for neutra l functiona l -differentia l -a l gebraic systems is considered. Necessary and sufficient con ditions under which these methods are consistent with the prob l em are estab l ished. The order of consistency is discussed. A convergence theorem for a genera l c l ass of methods is proved.
{"title":"Convergence of numerical methods for systems of neutral functional-differential-algebraic equations","authors":"T. Jankowski, M. Kwapisz","doi":"10.21136/am.1995.134307","DOIUrl":"https://doi.org/10.21136/am.1995.134307","url":null,"abstract":"Summary. A general class of numerical methods for solving initia l va l ue prob l ems for neutra l functiona l -differentia l -a l gebraic systems is considered. Necessary and sufficient con ditions under which these methods are consistent with the prob l em are estab l ished. The order of consistency is discussed. A convergence theorem for a genera l c l ass of methods is proved.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"19 1","pages":"457-472"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82254628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary. The fo l lowing three г e s u l t s for the g ene гal multivariate Ga u ss- M a r k o ff model with a s in g u la r covaгiance ma tri x aг e given or indicated. 1° deteгminant гa tio s as products o f independent chi-square distributions, 2° moments for the deteгminants and 3° the method o f obtaining appгoximate densities o f the deteгminants. s in g u la r covariance ma t г i x, set o f l ine aг parametric functions, moment o f determinant ratio, approximate simultaneous confidence interval
总结。本文给出或指出了以下3个模型的3个模型:1、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0、0。1°deteгminant гa是独立卡方分布的乘积，2°弯矩是deteгminants, 3°是获得deteгminants密度的方法。s g u r协方差马tг我x,设置o f线г参数功能,时刻o f行列式比率,同时近似置信区间
{"title":"Densities of determinant ratios, their moments and some simultaneous confidence intervals in the multivariate Gauss-Markoff model","authors":"W. Oktaba","doi":"10.21136/AM.1995.134277","DOIUrl":"https://doi.org/10.21136/AM.1995.134277","url":null,"abstract":"Summary. The fo l lowing three г e s u l t s for the g ene гal multivariate Ga u ss- M a r k o ff model with a s in g u la r covaгiance ma tri x aг e given or indicated. 1° deteгminant гa tio s as products o f independent chi-square distributions, 2° moments for the deteгminants and 3° the method o f obtaining appгoximate densities o f the deteгminants. s in g u la r covariance ma t г i x, set o f l ine aг parametric functions, moment o f determinant ratio, approximate simultaneous confidence interval","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"33 1","pages":"47-54"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91146107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary. A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).
{"title":"A simple model of thermoelectric oscillations","authors":"G. Cimatti, E. Feireisl","doi":"10.21136/AM.1995.134285","DOIUrl":"https://doi.org/10.21136/AM.1995.134285","url":null,"abstract":"Summary. A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"1 1","pages":"147-158"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80493523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary. A nonlinear differential system for describing an air-water system in ground water hydrology is given. The system is written in a fractional fl o w formulation, i.e., in terms o f a saturation and a gl oba l pressure. A continuous-time version o f the finite element method is developed and analyzed for the approximation o f the saturation and pressure. The saturation equation i s treated by a Galerkin finite element method, w h il e the pressure equation is treated by a mixed fi n i te element method. The analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive, and is then extended to a degenerate case where the diffusion coefficient can be zero. It is shown that error estimates o f optimal order in the L 2 -norm and almost optimal order in the L °°- nor m can be obtained i n the nondegenerate case. In the degenerate case w e consider a regularization o f the saturation equation by perturbing the diffusion coefficient. The norm o f error estimates depends on the severity o f the degeneracy in diffusivity, with almost optimal order convergence for non-severe degeneracy. Existence and uniqueness o f the approximate solution is also proven.
{"title":"Continuous-time finite element analysis of multiphase flow in groundwater hydrology","authors":"Zhangxin Chen, M. Espedal, R. Ewing","doi":"10.21136/AM.1995.134291","DOIUrl":"https://doi.org/10.21136/AM.1995.134291","url":null,"abstract":"Summary. A nonlinear differential system for describing an air-water system in ground water hydrology is given. The system is written in a fractional fl o w formulation, i.e., in terms o f a saturation and a gl oba l pressure. A continuous-time version o f the finite element method is developed and analyzed for the approximation o f the saturation and pressure. The saturation equation i s treated by a Galerkin finite element method, w h il e the pressure equation is treated by a mixed fi n i te element method. The analysis is carried out first for the case where the capillary diffusion coefficient is assumed to be uniformly positive, and is then extended to a degenerate case where the diffusion coefficient can be zero. It is shown that error estimates o f optimal order in the L 2 -norm and almost optimal order in the L °°- nor m can be obtained i n the nondegenerate case. In the degenerate case w e consider a regularization o f the saturation equation by perturbing the diffusion coefficient. The norm o f error estimates depends on the severity o f the degeneracy in diffusivity, with almost optimal order convergence for non-severe degeneracy. Existence and uniqueness o f the approximate solution is also proven.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"25 1","pages":"203-226"},"PeriodicalIF":0.7,"publicationDate":"1994-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87262088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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