794 research outputs found
Summation-By-Parts Operators and High-Order Quadrature
Summation-by-parts (SBP) operators are finite-difference operators that mimic
integration by parts. This property can be useful in constructing energy-stable
discretizations of partial differential vequations. SBP operators are defined
by a weight matrix and a difference operator, with the latter designed to
approximate to a specified order of accuracy. The accuracy of the weight
matrix as a quadrature rule is not explicitly part of the SBP definition. We
show that SBP weight matrices are related to trapezoid rules with end
corrections whose accuracy matches the corresponding difference operator at
internal nodes. The accuracy of SBP quadrature extends to curvilinear domains
provided the Jacobian is approximated with the same SBP operator used for the
quadrature. This quadrature has significant implications for SBP-based
discretizations; for example, the discrete norm accurately approximates the
norm for functions, and multi-dimensional SBP discretizations
accurately mimic the divergence theorem.Comment: 18 pages, 3 figure
A direct procedure for interpolation on a structured curvilinear two-dimensional grid
A direct procedure is presented for locally bicubic interpolation on a structured, curvilinear, two-dimensional grid. The physical (Cartesian) space is transformed to a computational space in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. Required partial derivative information is obtained by finite differences in the computational space. The partial derivatives in physical space are determined by repeated application of the chain rule for partial differentiation. A bilinear transformation is used to analytically transform the individual quadrilateral cells in physical space into unit squares. The interpolation is performed within each unit square using a piecewise bicubic spline
Die virale Gastroenteritis
Zusammenfassung: Viren sind die häufigste Ursache der akuten Gastroenteritis und nicht nur in den Entwicklungsländern ein Problem. Rotaviren bilden bei Säuglingen und Kleinkindern und Noroviren in allen Altersgruppen die Haupterreger. Neben sporadischen Fällen verursachen sie auch bei uns Epidemien in Krankenhäusern, Pflegeheimen, Schulen, Kinderkrippen, Hotels und Restaurants. Während die medizinische Betreuung sporadischer Fälle außer bei Säuglingen kaum Probleme bietet, ist das Management bei Epidemien aufwändig und zeitraubend. Der vorliegende Beitrag ist eine Übersicht über die wichtigsten Erreger, deren Pathogenese, Therapie und die krankenhaushygienische Betreuun
Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra
We present an extension of the summation-by-parts (SBP) framework to
tensor-product spectral-element operators in collapsed coordinates. The
proposed approach enables the construction of provably stable discretizations
of arbitrary order which combine the geometric flexibility of unstructured
triangular and tetrahedral meshes with the efficiency of sum-factorization
algorithms. Specifically, a methodology is developed for constructing
triangular and tetrahedral spectral-element operators of any order which
possess the SBP property (i.e. satisfying a discrete analogue of integration by
parts) as well as a tensor-product decomposition. Such operators are then
employed within the context of discontinuous spectral-element methods based on
nodal expansions collocated at the tensor-product quadrature nodes as well as
modal expansions employing Proriol-Koornwinder-Dubiner polynomials, the latter
approach resolving the time step limitation associated with the singularity of
the collapsed coordinate transformation. Energy-stable formulations for
curvilinear meshes are obtained using a skew-symmetric splitting of the metric
terms, and a weight-adjusted approximation is used to efficiently invert the
curvilinear modal mass matrix. The proposed schemes are compared to those using
non-tensorial multidimensional SBP operators, and are found to offer comparable
accuracy to such schemes in the context of smooth linear advection problems on
curved meshes, but at a reduced computational cost for higher polynomial
degrees.Comment: 26 pages, 5 figure
Aerodynamic computations using the convective-upstream split-pressure scheme with local preconditioning
Local Epitaxial Overgrowth for Stacked Complementary MOS Transistor Pairs
A three-dimensional silicon processing technology for CMOS circuits was developed and characterized. The first fully depleted SOI devices with individually biasable gates on both sides of the silicon film were realized. A vertically stacked CMOS Inverter built by lateral overgrowth was reported for the first time. Nucleation-free epitaxial lateral overgrowth of silicon over thin oxides was developed for both a pancake and a barrel-type epitaxy reactor: This process was optimized to limit damage to gate oxides and minimize dopant diffusion within the Substrate. Autodoping from impurities of the MOS transistors built in the substrate was greatly reduced. A planarisation technique was developed to reduce the silicon film thickness from 13μm to below 0.5μm for full depletion. Chemo-mechanical polishing was modified to yield an automatic etch stop with the corresponding control and uniformity of the silicon film. The resulting wafer topography is more planar than in a conventional substrate CMOS process. PMOS transistors which match the current drive of bulk NM0S devices of equal geometry were characterized, despite the three-times lower hole mobility. Devices realized in the substrate, at the bottom and on top of the SOI film were essentially indistinguishable from bulk devices. A novel device with two insulated gates controlling the same channel was characterized. Inverters were realized both as joint-gate configuration and with symmetric performance of n- and p-channel. These circuits were realized in the area of a single NMOS transistor
- …