Arbitrary-order fractance approximation circuits with high order-stability characteristic and wider approximation frequency bandwidth

2020 ◽  
pp. 1-12
Author(s):  
Qiu-Yan He ◽  
Yi-Fei Pu ◽  
Bo Yu ◽  
Xiao Yuan
Keyword(s):  
Arbitrary Order ◽  
High Order ◽  
Stability Characteristic ◽  
Frequency Bandwidth

scholarly journals High-Accuracy Treecode Based on Pseudoparticle Multipole Method

2003 ◽  
Vol 208 ◽  
pp. 305-314 ◽  
Author(s):  
Atsushi Kawai ◽  
Junichiro Makino
Keyword(s):  
Arbitrary Order ◽  
Scaling Up ◽  
Multipole Expansion ◽  
High Accuracy ◽  
High Order ◽  
Point Mass ◽  
Linear Scaling ◽  
Multipole Method ◽  
Primary Advantage

We invented the pseudoparticle multipole method (P2M2), a method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of P2M2 is that it works on GRAPE. Although the treecode has been implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can calculate forces from point-mass particles only. Thus the calculation cost grows quickly when high accuracy is required. With P2M2, the multipole expansion is expressed by particles, and thus GRAPE can calculate high order terms. Using P2M2, we realized arbitrary-order treecode on MDGRAPE-2. Timing result shows MDGRAPE-2 accelerates the calculation by a factor between 20 (for low accuracy) to 150 (for high accuracy). We parallelized the code so that it runs on MDGRAPE-2 cluster. The calculation speed of the code shows close-to-linear scaling up to 16 processors for N ≳ 106.

scholarly journals Geometric aspects of high-order eigenvalue problems I. Structures on spaces of boundary conditions

2004 ◽  
Vol 2004 (13) ◽  
pp. 647-678 ◽  
Author(s):  
Xifang Cao ◽  
Hongyou Wu
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Complex Number ◽  
Geometric Structure ◽  
Eigenvalue Problems ◽  
Arbitrary Order ◽  
High Order ◽  
Manifold Structure ◽  
Complex Boundary ◽  
Quasidifferential Equation

We consider some geometric aspects of regular eigenvalue problems of an arbitrary order. First, we clarify a natural geometric structure on the space of boundary conditions. This structure is the base for studying the dependence of eigenvalues on the boundary condition involved, and reveals new properties of these eigenvalues. Then, we solve the selfadjointness condition explicitly and obtain a manifold structure on the space of selfadjoint boundary conditions and several other consequences. Moreover, we give complete characterizations of several subsets of boundary conditions such as the set of all complex boundary conditions having a given complex number as an eigenvalue, and describe some of them topologically. The shapes of some of these subsets are shown to be independent of the quasidifferential equation in question.

scholarly journals Numerical Regularized Moment Method For High Mach Number Flow

2012 ◽  
Vol 11 (5) ◽  
pp. 1415-1438 ◽  
Author(s):  
Zhenning Cai ◽  
Ruo Li ◽  
Yanli Wang
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Moment Method ◽  
Arbitrary Order ◽  
High Order ◽  
Numerical Implementation ◽  
Moment System ◽  
Number Flow ◽  
High Mach ◽  
The Moment

AbstractThis paper is a continuation of our earlier work [SIAM J. Sci. Comput., 32(2010), pp. 2875-2907] in which a numerical moment method with arbitrary order of moments was presented. However, the computation may break down during the calculation of the structure of a shock wave with Mach number M0≥ 3. In this paper, we concentrate on the regularization of the moment systems. First, we apply the Maxwell iteration to the infinite moment system and determine the magnitude of each moment with respect to the Knudsen number. After that, we obtain the approximation of high order moments and close the moment systems by dropping some high-order terms. Linearization is then performed to obtain a very simple regularization term, thus it is very convenient for numerical implementation. To validate the new regularization, the shock structures of low order systems are computed with different shock Mach numbers.

scholarly journals Hyperbolicity of high-order systems of evolution equations

2015 ◽  
Vol 12 (01) ◽  
pp. 1-35 ◽  
Author(s):  
David Hilditch ◽  
Ronny Richter
Keyword(s):  
Evolution Equations ◽  
Arbitrary Order ◽  
Order Reduction ◽  
High Order ◽  
First Order ◽  
Definition Of ◽  
The Relationship

We study properties of evolution equations which are first order in time and arbitrary order in space (FTNS). Following Gundlach and Martín-García (2006) we define strong and symmetric hyperbolicity for FTNS systems and examine the relationship between these definitions, and the analogous concepts for first-order systems. We demonstrate equivalence of the FTNS definition of strong hyperbolicity with the existence of a strongly hyperbolic first-order reduction. We also demonstrate equivalence of the FTNS definition, up to N = 4, of symmetric hyperbolicity with the existence of a symmetric-hyperbolic first-order reduction.

New Extension of Affine Arithmetic: Complex Form

2012 ◽  
Vol 3 (1) ◽  
pp. 11
Author(s):  
Ahmed Elaraby Ahmed ◽  
Hassan El-Owny
Keyword(s):  
Arbitrary Order ◽  
Complex Form ◽  
Higher Order ◽  
Computational Approach ◽  
High Order ◽  
Affine Arithmetic ◽  
First Order ◽  
Order Extension

In this paper we present the new complex form for affine arithmetic (AA) which is a self-verifying computational approach that keeps track of first-order correlation between uncertainties in the data and intermediate and final results. In this paper we propose a higher-order extension satisfying the requirements of genericity, arbitrary-order and self-verification, comparing the resulting method with other wellknown high-order extensions of AA

Guidance Law Based on Differential Games for High Order Input Constrained Missile and Target

2008 ◽  
Author(s):  
Ilan Rusnak ◽  
Gyo¨rgy Hexner
Keyword(s):  
Energy Expenditure ◽  
Differential Games ◽  
Explicit Formula ◽  
Differential Game ◽  
Arbitrary Order ◽  
Transfer Functions ◽  
High Order ◽  
Minimum Phase ◽  
Guidance Law ◽  
Guidance Laws

The problem of derivation of guidance laws based on the differential games formalism for high order and acceleration constrained missile and target is formulated. The objective used is the minimaximization of the square of the miss and of the energy expenditure of the players. Explicit formula of the guidance law based on differential game formulation for unconstrained arbitrary order minimum or non-minimum phase is derived. For constrained players with this approach numerous cases emerge. For constrained players only implicit formulas of the GL are derivable. Each case has different structure of the implicit formulas. The cases that are treated-classified are created for different player’s transfer functions, i.e. missile or target autopilot transfer functions are minimum or non-minimum phase, respectively. Relatively tractable case is when the missile and the target are both minimum phase (or belong to a wider class of autopilot transfer functions with monotonous ramp response). For the case of constrained missile and target, implicit formula of the guidance law are derived and numerically solved. For minimum phase players one would guess, from results of one sided optimization, that the GL for constrained players would be obtained by limiting the acceleration commands derived as if there were not acceleration limits. It is shown that although this may be considered a practical-pragmatic solution it is strictly suboptimal.

scholarly journals Hybridization of Mixed High-Order Methods on General Meshes and Application to the Stokes Equations

2015 ◽  
Vol 15 (2) ◽  
pp. 111-134 ◽  
Author(s):  
Joubine Aghili ◽  
Sébastien Boyaval ◽  
Daniele A. Di Pietro
Keyword(s):  
Arbitrary Order ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Diffusion Problem ◽  
High Order ◽  
Two Space Dimensions ◽  
Primal Formulation ◽  
Scalar Diffusion ◽  
General Meshes ◽  
Theoretical Results

AbstractThis paper presents two novel contributions on the recently introduced Mixed High-Order (MHO) methods [`Arbitrary order mixed methods for heterogeneous anisotropic diffusion on general meshes', preprint (2013)]. We first address the hybridization of the MHO method for a scalar diffusion problem and obtain the corresponding primal formulation. Based on the hybridized MHO method, we then design a novel, arbitrary order method for the Stokes problem on general meshes. A full convergence analysis is carried out showing that, when independent polynomials of degree k are used as unknowns (at elements for the pressure and at faces for each velocity component), the energy-norm of the velocity and the L2-norm of the pressure converge with order (k + 1), while the L2-norm of the velocity (super-)converges with order (k + 2). The latter property is not shared by other methods based on a similar choice of unknowns. The theoretical results are numerically validated in two space dimensions on both standard and polygonal meshes.

Two-channel pitch/yaw missile autopilot design using arbitrary order sliding modes based pole placement

2015 ◽  
Vol 119 (1216) ◽  
pp. 765-779
Author(s):  
B. Kada
Keyword(s):  
Arbitrary Order ◽  
Sliding Mode ◽  
High Order ◽  
Design Tool ◽  
Pole Placement ◽  
Multivariable Systems ◽  
Sliding Modes ◽  
Order Pole ◽  
Strong Robustness ◽  
And Control

AbstractThe paper presents a new missile autopilot system design. The design is achieved through the pole-placement in quasi-continuous high-order sliding mode gains adjustment. Enhanced performance, strong robustness and smooth control are obtained through arbitrary increase of the number of non-oscillatory stable poles. The target application of this technique the two-channel pitch/yaw missile autopilot system is considered. Numerical simulations indicate that the arbitrary-order sliding modes based pole placement’s performance compares favourably against recently proposed high-order pole placement schemes.The proposed arbitrary-order pole placement scheme presents a promising design tool for finite-time stabilisation and control of uncertain multivariable systems.

scholarly journals A GENERAL COMPUTATION SCHEME FOR A HIGH-ORDER ASYMPTOTIC EXPANSION METHOD

2012 ◽  
Vol 15 (06) ◽  
pp. 1250044 ◽  
Author(s):  
AKIHIKO TAKAHASHI ◽  
KOHTA TAKEHARA ◽  
MASASHI TODA
Keyword(s):  
Asymptotic Expansion ◽  
Arbitrary Order ◽  
Diffusion Processes ◽  
Expansion Method ◽  
High Order ◽  
Analytic Approximation ◽  
Calculation Algorithm ◽  
Diffusion Type ◽  
Conditional Expectations ◽  
Asymptotic Expansion Method

This paper presents a new computational scheme for an asymptotic expansion method of an arbitrary order. The asymptotic expansion method in finance initiated by Kunitomo and Takahashi (1992), Yoshida (1992b) and Takahashi (1995, 1999) is a widely applicable methodology for an analytic approximation of expectation of a certain functional of diffusion processes. Hence, not only academic researchers but also many practitioners have used the methodology for a variety of financial issues such as pricing or hedging complex derivatives under high-dimensional underlying stochastic environments. In practical applications of the expansion, a crucial step is calculation of conditional expectations for a certain kind of Wiener functionals. Takahashi (1995, 1999) and Takahashi and Takehara (2007) provided explicit formulas for those conditional expectations necessary for the asymptotic expansion up to the third order. This paper presents the new method for computing an arbitrary-order expansion in a general diffusion-type stochastic environment, which is powerful especially for high-order expansions: We develops a new calculation algorithm for computing coefficients of the expansion through solving a system of ordinary differential equations that is equivalent to computing the conditional expectations directly. To demonstrate its effectiveness, the paper gives numerical examples of the approximation for a λ-SABR model up to the fifth order.

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