Stable multilevel splittings of boundary edge element spaces

We establish the stability of nodal multilevel decompositions of lowest-order conforming boundary element subspaces of the trace space ${\boldsymbol{H}}^{-\frac {1}{2}}(\operatorname {div}_{\varGamma },{\varGamma })$ of ${\boldsymbol{H}}(\operatorname {\bf curl},{\varOmega })$ on boundaries of triangulated Lipschitz polyhedra. The decompositions are based on nested triangular meshes created by uniform refinement and the stability bounds are uniform in the number of refinement levels. The main tool is the general theory of P.Oswald (Interface preconditioners and multilevel extension operators, in Proc. 11th Intern. Conf. on Domain Decomposition Methods, London, 1998, pp.96-103) that teaches, when stability of decompositions of boundary element spaces with respect to trace norms can be inferred from corresponding stability results for finite element spaces. ${\boldsymbol{H}}(\operatorname {\bf curl},{\varOmega })$ -stable discrete extension operators are instrumental in this. Stable multilevel decompositions immediately spawn subspace correction preconditioners whose performance will not degrade on very fine surface meshes. Thus, the results of this article demonstrate how to construct optimal iterative solvers for the linear systems of equations arising from the Galerkin edge element discretization of boundary integral equations for eddy current problem

Error Analysis of a Fully Discrete Projection Method for Magnetohydrodynamic System

In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi-implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H(curl) conforming Nédélec edge elements are used to approximate the magnetic equation. One key point of the projection method is to be compatible with two different spaces for calculating velocity, which leads one to obtain the pressure by solving a Poisson equation. The results show that the proposed projection scheme meets a discrete energy stability. In addition, with the help of a proper regularity hypothesis for the exact solution, this paper provides a rigorous optimal error analysis of velocity, pressure and magnetic induction. Finally, several numerical examples are performed to demonstrate both accuracy and efficiency of our proposed scheme

The Genetic Mechanism of Inertinite in the Middle Jurassic Inertinite-Rich Coal Seams of the Southern Ordos Basin

Inertinite is an important type of organic maceral in coal deposits, andalso an important geological information carrier of coal forming environments. In the southern section of the Ordos Basin, the No. 4 inertinite-richcoal seam of the Middle Jurassic Yan’an Formation in the Binchang Coalfield was selected as an example to study the genetic mechanism of theinertinite. In this study, the results obtained from experimental tests ofcoal rock, including principal and trace elements, stable carbon isotopes,scanning electron microscopy, inertinite reflectance, sporopollen andfree radical retorting methods, were analyzed. Then, the findings werecombined with the previous understanding of the oxygen content in theatmosphere and ground fire characteristics, in order to discuss the genesismechanism of inertinite in the No. 4 coal seam. The obtained researchresults were as follows: (1) During the coal forming period of the No. 4coal seam, the overall climate had been relatively dry. There were fourrelatively dry-wet climate cycles in the No.4 coal seam, which werecontrolled by the eccentricity astronomical period. The inertinite contentwere relatively high during the dry periods; (2) The temperature rangesuitable for microorganism activities during the oxidation processes wasbetween 0 and 80℃ . The simulation results of the free radical concentrations showed that the maximum temperature of fusain in the No. 4 coalseam during the process of coalification had not exceeded 300℃ , whichwas significantly higher than the temperature range of microorganismactivities. Therefore, these were not conducive to the activities of microorganism and formation of inertinite during the coal-forming period;(3) The genesis temperature of the inertinite in the No. 4 coal seam wascalculated according to the reflectance of the inertinite, which was lowerthan 400 ℃ . This result supported the cause of wildfire of the inertiniteand reflected that the type of wildfire was mainly ground fire, along withpartially surface fire. Moreover, the paleogeographic location, climaticconditions, atmospheric oxygen concentration, etc. of the study areashowed that the conditions for wildfire events were in fact available; (4)There were dense and scattered fusinite observed in the No. 4 coal seam,and the thickness of cell walls were found to differ. It was speculated thatthis was related to the type of wildfire, combustion temperatures, combustion timeframes, and different initial conditions of the burned objectsduring the coal forming periods

A convergent adaptive finite element method with optimal complexity

preprin

A Case for Leveraging 802.11p for Direct Phone-to-Phone Communications

WiFi cannot effectively handle the demands of device-to-device communication between phones, due to insufficient range and poor reliability. We make the case for using IEEE 802.11p DSRC instead, which has been adopted for vehicle-to-vehicle communications, providing lower latency and longer range. We demonstrate a prototype motivated by a novel fabrication process that deposits both III-V and CMOS devices on the same die. In our system prototype, the designed RF front-end is interfaced with a baseband processor on an FPGA, connected to Android phones. It consumes 0.02uJ/bit across 100m assuming free space. Application-level power control dramatically reduces power consumption by 47-56%.Singapore-MIT Alliance for Research and TechnologyAmerican Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

An optimally convergent adaptive mixed finite element method

International audienceWe prove convergence and optimal complexity of an adaptive mixed finite element algorithm, based on the lowest-order Raviart–Thomas finite element space. In each step of the algorithm, the local refinement is either performed using simple edge residuals or a data oscillation term, depending on an adaptive marking strategy. The inexact solution of the discrete system is controlled by an adaptive stopping criterion related to the estimator

Quasi-optimality of adaptive non-conforming finite element methods for the Stokes equations

International audienc

On the error bounds of nonconforming finite elements

International audienc

Stable multilevel splittings of boundary edge element spaces

ISSN:0006-3835ISSN:1572-912

Convergence and quasi-optimal complexity of a simple adaptive finite element method

We prove convergence and quasi-optimal complexity of an adaptive finite element algorithm on triangular meshes with standard mesh refinement. Our algorithm is based on an adaptive marking strategy. In each iteration, a simple edge estimator is compared to an oscillation term and the marking of cells for refinement is done according to the dominant contribution only. In addition, we introduce an adaptive stopping criterion for iterative solution which compares an estimator for the iteration error with the estimator for the discretization error