The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent ...The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.展开更多
Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method （SEM） using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time dom...Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method （SEM） using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient （PCG）-element by element （EBE） method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method （FDM） for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.展开更多
The technical and economic optimization of road projects has led to research into the use of materials obtained by mechanical stabilization for pavement construction. This research has enabled us to outline a solution...The technical and economic optimization of road projects has led to research into the use of materials obtained by mechanical stabilization for pavement construction. This research has enabled us to outline a solution capable of giving the sub-base layer the necessary and sufficient capacity to support the induced loads forecast for the traffic. This work evaluates the effect of adding fine silty clay (Cl) and clayey silt (Csp), two corrective materials to alluvial gravel (0/14), the main material, in the process of improving its cohesion and geotechnical properties. The results obtained show that the optimum mix is obtained with 10% by weight of Cl and 15% Csp. The granulometry of the mixes is spread out, but poorly calibrated. The Ag-Cl mixtures made at 10%, 15%, 20%, 25% 30% and Ag-Csp at 15%, 20%, 25%, 30%, and 35%, do not obey the law of mixtures. Mixing with 10% Cl reduces the sand equivalent of alluvial gravel by 60.23%, while mixing with 15% Cl reduces the sand equivalent by 6.82%. The addition of correctors increases the optimum water content and fine sand content of the mixes. Increasing the fine sand content reduces the optimum dry density, CBR index and static modulus. Mixes containing 10% Cl and 15% Csp have CBR values of CBRCl (96%) and CBRCsp (84%) and are not suitable for pavement base layers. In fact, the hardness of the grains has a Los Anges value of 41%, higher than the maximum permitted by the standard of 35%. The mixes obtained can be used as pavement base layers for traffic levels in a cumulative number of heavy goods vehicles 5 × 105 6 for an approximate life of 15 years.展开更多
文摘The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.
基金supported by the National Natural Science Foundation of China(Grant No.40774099,10874202)the National High Technology Research and Development Program of China(Grant No.2008AA06Z205)
文摘Based on strong and weak forms of elastic wave equations, a Chebyshev spectral element method （SEM） using the Galerkin variational principle is developed by discretizing the wave equation in the spatial and time domains and introducing the preconditioned conjugate gradient （PCG）-element by element （EBE） method in the spatial domain and the staggered predictor/corrector method in the time domain. The accuracy of our proposed method is verified by comparing it with a finite-difference method （FDM） for a homogeneous solid medium and a double layered solid medium with an inclined interface. The modeling results using the two methods are in good agreement with each other. Meanwhile, to show the algorithm capability, the suggested method is used to simulate the wave propagation in a layered medium with a topographic traction free surface. By introducing the EBE algorithm with an optimized tensor product technique, the proposed SEM is especially suitable for numerical simulation of wave propagations in complex models with irregularly free surfaces at a fast convergence rate, while keeping the advantage of the finite element method.
文摘The technical and economic optimization of road projects has led to research into the use of materials obtained by mechanical stabilization for pavement construction. This research has enabled us to outline a solution capable of giving the sub-base layer the necessary and sufficient capacity to support the induced loads forecast for the traffic. This work evaluates the effect of adding fine silty clay (Cl) and clayey silt (Csp), two corrective materials to alluvial gravel (0/14), the main material, in the process of improving its cohesion and geotechnical properties. The results obtained show that the optimum mix is obtained with 10% by weight of Cl and 15% Csp. The granulometry of the mixes is spread out, but poorly calibrated. The Ag-Cl mixtures made at 10%, 15%, 20%, 25% 30% and Ag-Csp at 15%, 20%, 25%, 30%, and 35%, do not obey the law of mixtures. Mixing with 10% Cl reduces the sand equivalent of alluvial gravel by 60.23%, while mixing with 15% Cl reduces the sand equivalent by 6.82%. The addition of correctors increases the optimum water content and fine sand content of the mixes. Increasing the fine sand content reduces the optimum dry density, CBR index and static modulus. Mixes containing 10% Cl and 15% Csp have CBR values of CBRCl (96%) and CBRCsp (84%) and are not suitable for pavement base layers. In fact, the hardness of the grains has a Los Anges value of 41%, higher than the maximum permitted by the standard of 35%. The mixes obtained can be used as pavement base layers for traffic levels in a cumulative number of heavy goods vehicles 5 × 105 6 for an approximate life of 15 years.
