Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is ac...Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest.A sec- ond,less-popular method of spatial adaptivity is called'mesh motion'(r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales.This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function,the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone.Further,in an attempt to support the requirements of a very general class of climate simulation applications,the proposed method is de- signed to accommodate unstructured,polygonal mesh topologies in addition to the most popular mesh types.展开更多
The need to perform spatial queries and searches is commonly encountered within the field of computational physics.The development of applications ranging from scientific visualization to finite element analysis requi...The need to perform spatial queries and searches is commonly encountered within the field of computational physics.The development of applications ranging from scientific visualization to finite element analysis requires efficient methods of locating domain objects relative to general locations in space.Much of the time,it is possible to form and maintain spatial relationships between objects either explicitly or by using relative motion constraints as the application evolves in time.Occasionally,either due to unpredictable relative motion or the lack of state information,an application must perform a general search(or ordering)of geometric objects without any explicit spatial relationship information as a basis.If previous state information involving domain geometric objects is not available,it is typically an involved and time consuming process to create object adjacency information or to order the objects in space.Further,as the number of objects and the spatial dimension of the problem domain is increased,the time required to search increases greatly.This paper proposes an implementation of a spatial k-d tree(skD-tree)for use by various applications when a general domain search is required.The skD-tree proposed in this paper is a spatial access method where successive tree levels are split along different dimensions.Objects are indexed by their centroid,and the minimum bounding box of objects in a node are stored in the tree node.The paper focuses on a discussion of efficient and practical algorithms for multidimensional spatial data structures for fast spatial query processing.These functions include the construction of a skD-tree of geometric objects,intersection query,containment query,and nearest neighbor query operations.展开更多
文摘Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest.A sec- ond,less-popular method of spatial adaptivity is called'mesh motion'(r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales.This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function,the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone.Further,in an attempt to support the requirements of a very general class of climate simulation applications,the proposed method is de- signed to accommodate unstructured,polygonal mesh topologies in addition to the most popular mesh types.
基金by contractors of the U.S.Government under Contract Nos.DE-AC05-00OR22725 and DE-AC07-05ID14517.
文摘The need to perform spatial queries and searches is commonly encountered within the field of computational physics.The development of applications ranging from scientific visualization to finite element analysis requires efficient methods of locating domain objects relative to general locations in space.Much of the time,it is possible to form and maintain spatial relationships between objects either explicitly or by using relative motion constraints as the application evolves in time.Occasionally,either due to unpredictable relative motion or the lack of state information,an application must perform a general search(or ordering)of geometric objects without any explicit spatial relationship information as a basis.If previous state information involving domain geometric objects is not available,it is typically an involved and time consuming process to create object adjacency information or to order the objects in space.Further,as the number of objects and the spatial dimension of the problem domain is increased,the time required to search increases greatly.This paper proposes an implementation of a spatial k-d tree(skD-tree)for use by various applications when a general domain search is required.The skD-tree proposed in this paper is a spatial access method where successive tree levels are split along different dimensions.Objects are indexed by their centroid,and the minimum bounding box of objects in a node are stored in the tree node.The paper focuses on a discussion of efficient and practical algorithms for multidimensional spatial data structures for fast spatial query processing.These functions include the construction of a skD-tree of geometric objects,intersection query,containment query,and nearest neighbor query operations.
