| http://dbpedia.org/ontology/abstract
|
The Kansa method is a computer method used … The Kansa method is a computer method used to solve partial differential equations. Its main advantage is it is very easy to understand and program on a computer. It is much less complicated than the finite elementmethod. Another advantage is it works well on multi variable problems. The finite element method is complicated when working with more than 3 space variables and time. The Kansa Method can be explained by an analogy to a basketball court with many light bulbs suspended all across the ceiling. You solve for the brightness of each bulb so that the desired light intensity directly on the floor of the basketball court under each bulb solves the differential equation at that point. So if the basketball court has 100 bulbs suspended over it; the light intensity at any point on the floor of the basketball courtapproaches a light intensity that approximately solves the differential equation at any location on the floor of the basketball court. A simple computer program can solve by iteration for the brightness of each bulb, which makes this method easy to program. This method does not need weighted residuals (galerkin), integration, or advanced mathematics. E. J. Kansa in very early 1990s made the first attempt to extend radial basis function (RBF), which was then quite popular in scattered data processing and function approximation, to the solution of partial differential equations in the strong-form collocation formulation. His RBF collocation approach is inherently meshless, easy-to-program, and mathematically very simple to learn. Before long, this method is known as the Kansa method in academic community. Because the RBF uses the one-dimensional Euclidean distance variable irrespective of dimensionality, the Kansa method is independent of dimensionality and geometric complexity of problems of interest. The method is a domain-type numerical technique in the sense that the problem is discretized not only on the boundary to satisfy boundary conditions but also inside domain to satisfy governing equation. In contrast, there is another type of RBF numerical methods, called boundary-type RBF collocation method, such as the method of fundamental solution, boundary knot method, singular boundary method, boundary particle method, and regularized meshless method, in which the basis functions, also known as kernel function, satisfy the governing equation and are often fundamental solution or general solution of governing equation. Consequently, only boundary discretization is required. Since the RBF in the Kansa method does not necessarily satisfy the governing equation, one has more freedom to choose a RBF. The most popular RBF in the Kansa method is the multiquadric (MQ), which usually shows spectral accuracy if an appropriate shape parameter is chosen. an appropriate shape parameter is chosen.
, 20世纪90年代，E. J. Kansa将用于散乱数据处理和函数近似的径向基函数用于 … 20世纪90年代，E. J. Kansa将用于散乱数据处理和函数近似的径向基函数用于处理偏微分方程，并提出一种强格式的配点方法。Kansa所提出的径向基函数配点方法是真正的无网格方法，具有易于编程、数学形式简单、方便掌握等优点。该方法提出后不久，被学术界称之为Kansa方法(Kansa method)。 由于径向基函数是采用无需考虑维数的一维欧几里德距离作为变量，Kansa方法适用于高维的和形状复杂的问题。Kansa方法是一种区域型方法，不仅在边界离散使其满足边界条件，同时内部配点需要满足控制方程。 此外，还有一类以径向基函数为核函数的边界型径向基函数配点方法（Boundary-type RBF collocation method），如、边界节点法、奇异边界法、边界粒子法、和正则化无网格法（Regularized meshless method）等。这类方法选取的基函数（也被称为核函数），通常选取控制方程的基本解或通解，因而满足控制方程。因此只需要在边界离散满足边界条件即可。 Kansa方法选取的径向基函数不需要满足控制方程，因此选取基函数有更大的自由空间。多元二次曲面(Multiquadric, MQ)函数是Kansa方法最常用的径向基函数，如果选择了恰当的形参数可以获得谱收敛的精度。函数是Kansa方法最常用的径向基函数，如果选择了恰当的形参数可以获得谱收敛的精度。
|
| http://dbpedia.org/ontology/wikiPageExternalLink
|
https://web.archive.org/web/20121128025959/http:/em.hhu.edu.cn/chenwen/html/MKM.htm +
|
| http://dbpedia.org/ontology/wikiPageID
|
35705190
|
| http://dbpedia.org/ontology/wikiPageLength
|
12762
|
| http://dbpedia.org/ontology/wikiPageRevisionID
|
1043763421
|
| http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Partial_differential_equations +
, http://dbpedia.org/resource/Boundary_knot_method +
, http://dbpedia.org/resource/Finite_element_method +
, http://dbpedia.org/resource/Singular_boundary_method +
, http://dbpedia.org/resource/Method_of_fundamental_solutions +
, http://dbpedia.org/resource/Boundary_value_problem +
, http://dbpedia.org/resource/Category:Partial_differential_equations +
, http://dbpedia.org/resource/Method_of_fundamental_solution +
, http://dbpedia.org/resource/Radial_basis_function +
, http://dbpedia.org/resource/Boundary_element_method +
, http://dbpedia.org/resource/Boundary_particle_method +
|
| http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Reflist +
|
| http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Partial_differential_equations +
|
| http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Kansa_method?oldid=1043763421&ns=0 +
|
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Kansa_method +
|
| owl:sameAs |
https://global.dbpedia.org/id/4osAz +
, http://yago-knowledge.org/resource/Kansa_method +
, http://www.wikidata.org/entity/Q6364428 +
, http://rdf.freebase.com/ns/m.0jt3p_4 +
, http://dbpedia.org/resource/Kansa_method +
, http://zh.dbpedia.org/resource/Kansa%E6%96%B9%E6%B3%95 +
|
| rdf:type |
http://dbpedia.org/class/yago/Equation106669864 +
, http://dbpedia.org/class/yago/WikicatPartialDifferentialEquations +
, http://dbpedia.org/class/yago/Communication100033020 +
, http://dbpedia.org/class/yago/Message106598915 +
, http://dbpedia.org/class/yago/DifferentialEquation106670521 +
, http://dbpedia.org/class/yago/Statement106722453 +
, http://dbpedia.org/class/yago/MathematicalStatement106732169 +
, http://dbpedia.org/class/yago/Abstraction100002137 +
, http://dbpedia.org/class/yago/PartialDifferentialEquation106670866 +
|
| rdfs:comment |
20世纪90年代，E. J. Kansa将用于散乱数据处理和函数近似的径向基函数用于 … 20世纪90年代，E. J. Kansa将用于散乱数据处理和函数近似的径向基函数用于处理偏微分方程，并提出一种强格式的配点方法。Kansa所提出的径向基函数配点方法是真正的无网格方法，具有易于编程、数学形式简单、方便掌握等优点。该方法提出后不久，被学术界称之为Kansa方法(Kansa method)。 由于径向基函数是采用无需考虑维数的一维欧几里德距离作为变量，Kansa方法适用于高维的和形状复杂的问题。Kansa方法是一种区域型方法，不仅在边界离散使其满足边界条件，同时内部配点需要满足控制方程。 此外，还有一类以径向基函数为核函数的边界型径向基函数配点方法（Boundary-type RBF collocation method），如、边界节点法、奇异边界法、边界粒子法、和正则化无网格法（Regularized meshless method）等。这类方法选取的基函数（也被称为核函数），通常选取控制方程的基本解或通解，因而满足控制方程。因此只需要在边界离散满足边界条件即可。 Kansa方法选取的径向基函数不需要满足控制方程，因此选取基函数有更大的自由空间。多元二次曲面(Multiquadric, MQ)函数是Kansa方法最常用的径向基函数，如果选择了恰当的形参数可以获得谱收敛的精度。函数是Kansa方法最常用的径向基函数，如果选择了恰当的形参数可以获得谱收敛的精度。
, The Kansa method is a computer method used … The Kansa method is a computer method used to solve partial differential equations. Its main advantage is it is very easy to understand and program on a computer. It is much less complicated than the finite elementmethod. Another advantage is it works well on multi variable problems. The finite element method is complicated when working with more than 3 space variables and time.with more than 3 space variables and time.
|
| rdfs:label |
Kansa method
, Kansa方法
|
