We consider the modeling and simulation by means of multiwavelets on many patches. Our focus is on molecular surfaces which are represented in the form of Solvent Excluded Surfaces that are featured by smooth blending...We consider the modeling and simulation by means of multiwavelets on many patches. Our focus is on molecular surfaces which are represented in the form of Solvent Excluded Surfaces that are featured by smooth blendings between the constituting atoms. The wavelet bases are constructed on the unit square which maps bijectively onto the patches embedded in the space. The cavity which designates the surface bounding a molecular model is acquired from the nuclei coordinates and the Van-der-Waals radii. We use multi-wavelets for which the wavelet basis functions are organized hierarchically on several levels. Our assembly of the linear system is accomplished by using a hierarchical tree which enables the treatment of large molecules admitting thousands of patches. Along with the patch construction, some wavelet simulation outcomes which are applied to realistic patches are reported.展开更多
A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator whi...A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator which turns out to be efficient and reliable. We demonstrate upper and lower bounds of the error estimator with respect to the exact accuracy. For the transmission problem, the coefficients for the internal and external domains can be highly dissimilar. One major difficulty is the characteristic of the estimator at the interface. The a-posteriori error estimates can be computed very efficiently element by element. To corroborate the theoretical analysis, we report on a few numerical results.展开更多
In the process of interpreting simulation results,new post-processing techniques are developed.This work presents a post-processing method that analyzes the solidification pattern formed by simulation of the solidific...In the process of interpreting simulation results,new post-processing techniques are developed.This work presents a post-processing method that analyzes the solidification pattern formed by simulation of the solidification process of molten metal in a mold to produce shaped castings.Simulations generally involve numerical solutions of differential equations which are discretized by dividing the three-dimensional computational domain into small finite volume elements using a 3D grid.The locations of the grid points and values of the solidification time at these locations are used to divide the spatial data into 3D sections such that starting from a hotspot location within the section that has high solidification time,there is a gradient outwards with lower values of solidification time.Each section is assumed to be fed by one or more feeders that must freeze only after the section has solidified completely.The volume of a feeder can be determined from the volume of the section it is supposed to feed.The volume and surface area of sections are determined approximately to calculate feeder size and dimensions.The post-processing algorithm is a simulation-based quantitative approach to feeder design which in conventional foundry practice has been more of an art than science.It is also general enough for use in other 3D segmentation applications.展开更多
文摘We consider the modeling and simulation by means of multiwavelets on many patches. Our focus is on molecular surfaces which are represented in the form of Solvent Excluded Surfaces that are featured by smooth blendings between the constituting atoms. The wavelet bases are constructed on the unit square which maps bijectively onto the patches embedded in the space. The cavity which designates the surface bounding a molecular model is acquired from the nuclei coordinates and the Van-der-Waals radii. We use multi-wavelets for which the wavelet basis functions are organized hierarchically on several levels. Our assembly of the linear system is accomplished by using a hierarchical tree which enables the treatment of large molecules admitting thousands of patches. Along with the patch construction, some wavelet simulation outcomes which are applied to realistic patches are reported.
文摘A higher order finite element method is considered to treat an interface problem. The polynomial degree is allowed to be arbitrary but it is fixed for the FEM-variational formulation. We propose an error estimator which turns out to be efficient and reliable. We demonstrate upper and lower bounds of the error estimator with respect to the exact accuracy. For the transmission problem, the coefficients for the internal and external domains can be highly dissimilar. One major difficulty is the characteristic of the estimator at the interface. The a-posteriori error estimates can be computed very efficiently element by element. To corroborate the theoretical analysis, we report on a few numerical results.
基金supported by the Aeronautical Research and Development Board of India under the grant DARO/08/1161319/M/I to National Institute for Interdisciplinary ScienceTechnology,Council of Scientific and Industrial Research(CSIR),India.
文摘In the process of interpreting simulation results,new post-processing techniques are developed.This work presents a post-processing method that analyzes the solidification pattern formed by simulation of the solidification process of molten metal in a mold to produce shaped castings.Simulations generally involve numerical solutions of differential equations which are discretized by dividing the three-dimensional computational domain into small finite volume elements using a 3D grid.The locations of the grid points and values of the solidification time at these locations are used to divide the spatial data into 3D sections such that starting from a hotspot location within the section that has high solidification time,there is a gradient outwards with lower values of solidification time.Each section is assumed to be fed by one or more feeders that must freeze only after the section has solidified completely.The volume of a feeder can be determined from the volume of the section it is supposed to feed.The volume and surface area of sections are determined approximately to calculate feeder size and dimensions.The post-processing algorithm is a simulation-based quantitative approach to feeder design which in conventional foundry practice has been more of an art than science.It is also general enough for use in other 3D segmentation applications.
