A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions,body forces,and time depending coefficients...A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions,body forces,and time depending coefficients is developed.For ensemble solutions in L_(∞)(0,T;L^(2)(Ω)),a superconvergent rate with respect to the freedom degree of the globally coupled unknowns for all the polynomials of degree k≥0 is established.The results of numerical experiments are consistent with the theoretical findings.展开更多
In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. Th...In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.展开更多
基金G.Chen was supported by National Natural Science Foundation of China(NSFC)(11801063)by China Postdoctoral Science Foundation(2018M633339,2019T120808)+1 种基金by the Fundamental Research Funds for the Central Universities(YJ202030)Y.Zhang was supported by US National Science Foundation(NSF)(DMS-1619904).
文摘A new second order time stepping ensemble hybridizable discontinuous Galerkin method for parameterized convection diffusion PDEs with various initial and boundary conditions,body forces,and time depending coefficients is developed.For ensemble solutions in L_(∞)(0,T;L^(2)(Ω)),a superconvergent rate with respect to the freedom degree of the globally coupled unknowns for all the polynomials of degree k≥0 is established.The results of numerical experiments are consistent with the theoretical findings.
基金supported by PRIN-MIUR-Cofin 2006,project,by"Progetti Strategici EF2006"University of Bologna,and by University of Bologna"Funds for selected research topics"
文摘In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.
