5,207 research outputs found
RBF multiscale collocation for second order elliptic boundary value problems
In this paper, we discuss multiscale radial basis function collocation methods for solving elliptic partial differential equations on bounded domains. The approximate solution is constructed in a multi-level fashion, each level using compactly supported radial basis functions of smaller scale on an increasingly fine mesh. On each level, standard symmetric collocation is employed. A convergence theory is given, which builds on recent theoretical advances for multiscale approximation using compactly supported radial basis functions. We are able to show that the convergence is linear in the number of levels. We also discuss the condition numbers of the arising systems and the effect of simple, diagonal preconditioners, now proving rigorously previous numerical observations
On explicit results at the intersection of the Z_2 and Z_4 orbifold subvarieties in K3 moduli space
We examine the recently found point of intersection between the Z_2 and Z_4
orbifold subvarieties in the K3 moduli space more closely. First we give an
explicit identification of the coordinates of the respective Z_2 and Z_4
orbifold theories at this point. Secondly we construct the explicit
identification of conformal field theories at this point and show the
orthogonality of the two subvarieties.Comment: Latex, 23 page
Computational model of one-dimensional flow of water in an unsaturated soil
O estudo do fluxo de água em zonas não saturadas do solo é de grande importância para pesquisas relacionadas à disponibilidade hÃdrica para o desenvolvimento das plantas. Devido ao alto custo, ao tempo demandado e ao esforço humano nas investigações de campo, os modelos matemáticos, aliados à s técnicas numéricas e avanços computacionais, constituem-se em uma ferramenta importante na previsão desses estudos. No presente trabalho, objetivou-se solucionar a equação diferencial parcial não linear de Richards mediante a aplicação do Método de Elementos Finitos. Na aproximação espacial, foi empregada a adaptatividade com refinamento "h" na malha de elementos finitos e, na derivada temporal, foi aplicado o esquema de Euler ExplÃcito. A função interpolação polinomial utilizada foi de grau 2, e a que garantiu a conservação de massa da estratégia de adaptação. Para a validação do modelo, foram utilizados dados disponÃveis em literatura. A utilização da função interpolação polinomial de grau 2 e o refinamento "h", com considerável redução do tempo de execução da rotina computacional, permitiram uma boa concordância do modelo em comparação a soluções disponÃveis na literatura.Study of water flow in the unsaturated soil zone is of great importance for research related to the water availability for crop development. Due to the high cost, the time required and the human effort in the field investigations, mathematical models combined with numerical techniques and computational advances are important tools in the prediction of these studies. This work aimed to solve the Richards's non-linear partial differential equation by applying the Finite Element Method. Adaptability with "h" refinement of the finite element mesh was used in the spatial approximation, while Explicit Euler scheme was applied for the time derivative. The polynomial interpolation function used was of degree two, and ensured the mass conservation of the adaptation strategy. To validate the model, data available in the literature were used. Use of the polynomial interpolation function with degree two and the "h" refinement, with considerable reduction of the computational runtime allowed good agreement in comparison to solutions available in the literature
Numerical Ricci-flat metrics on K3
We develop numerical algorithms for solving the Einstein equation on
Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler
parameters. We show that Kahler geometry can be exploited for significant gains
in computational efficiency. As a proof of principle, we apply our methods to a
one-parameter family of K3 surfaces constructed as blow-ups of the T^4/Z_2
orbifold with many discrete symmetries. High-resolution metrics may be obtained
on a time scale of days using a desktop computer. We compute various geometric
and spectral quantities from our numerical metrics. Using similar resources we
expect our methods to practically extend to Calabi-Yau three-folds with a high
degree of discrete symmetry, although we expect the general three-fold to
remain a challenge due to memory requirements.Comment: 38 pages, 10 figures; program code and animations of figures
downloadable from http://schwinger.harvard.edu/~wiseman/K3/ ; v2 minor
corrections, references adde
On the Dirichlet problem in elasticity for a domain exterior to an arc
AbstractWe consider here a Dirichlet problem for the two-dimensional linear elasticity equations in the domain exterior to an open arc in the plane. It is shown that the problem can be reduced to a system of boundary integral equations with the unknown density function being the jump of stresses across the arc. Existence, uniqueness as well as regularity results for the solution to the boundary integral equations are established in appropriate Sobolev spaces. In particular, asymptotic expansions concerning the singular behavior for the solution near the tips of the arc are obtained. By adding special singular elements to the regular splines as test and trial functions, an augmented Galerkin procedure is used for the corresponding boundary integral equations to obtain a quasi-optimal rate of convergence for the approximate solutions
Desempenho do feijoeiro comum em primeira safra e severidade de doenças em sistema agroecológico no Cerrado Goiano.
O presente trabalho teve por objetivos avaliar a produção de massa seca e quantidade de N produzidas por plantas de cobertura do solo, bem como seus efeitos, e de sistemas de manejo do solo, sobre a severidade de doenças e desempenho agronômico da cultura do feijoeiro comum de primeira safra
Produção de grãos e relação com reação a doenças em feijoeiro comum cultivado em sistema de manejo orgânico.
Este trabalho objetivou avaliar a produção de grãos do feijoeiro comum em sistema de manejo orgânico e os efeitos do crestamento bacteriano comum e da mancha angular sobre a produção do feijoeiro comum da cultivar BRS Supremo sob diferentes tipos de cultura de cobertura e manejo do solo
Produção de grãos em relação com reação a doenças em feijoeiro comum cultivado em sistema de manejo orgânico.
Este trabalho objetivou avaliar a produção de grãos do feijoeiro-comum em sistema de manejo orgânico e os efeitos do crestamento bacteriano comum e da mancha angular sobre a produção do feijoeiro-comum da cultivar BRS supremo sob diferentes tipos de cultura de cobertura e manejo do solo.CONAFE
Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations
We consider an inverse problem of determining coefficient matrices in an
-system of second-order elliptic equations in a bounded two dimensional
domain by a set of Cauchy data on arbitrary subboundary. The main result of the
article is as follows: If two systems of elliptic operators generate the same
set of partial Cauchy data on an arbitrary subboundary, then the coefficient
matrices of the first-order and zero-order terms satisfy the prescribed system
of first-order partial differential equations. The main result implies the
uniqueness of any two coefficient matrices provided that the one remaining
matrix among the three coefficient matrices is known
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