universal scaling behaviour for iterated maps in the complex plane according to the theory of schroder and siegel certain complex analytic maps possess a family of closed invariant curves in the complex plane we have made a numerical study of these curves by iterating the map and have found that the largest curve is a fractal when the winding number of the map is the golden mean the fractal curve has universal scaling properties and the scaling parameter differs from those found for other types of maps also for this winding number there are universal scaling functions which describe the behaviour asn of theq n th iterates of the map whereq n is thenth fibonacci number

calculating hausdorff dimension of julia sets and kleinian limit sets we present a new algorithm for efficiently computing the hausdorff dimension of sets x invariant under conformal expanding dynamical systems by locating the periodic points of period up to n we construct approximations s n which converge to dim x super exponentially fast in n this method can be used to give rigorous estimates for important examples including hyperbolic julia sets and limit sets of schottky and quasifuchsian groups

an optimized wave equation for seismic modeling and reverse time migration the acoustic wave equation has been widely used for the modeling and reverse time migration of seismic data numerical implementation of this equation via finite difference techniques has established itself as a valuable approach and has long been a favored choice in the industry to ensure quality results accurate approximations are required for spatial and time derivatives traditionally they are achieved numerically by using either relatively very fine computation grids or very long finite difference operators otherwise the numerical error known as numerical dispersion is present in the data and contaminates the signals however either approach will result in a considerable increase in the computational cost a simple and computationally low cost modification to the standard acoustic wave equation is presented to suppress numerical dispersion this dispersion attenuator is one analogy of the antialiasing operator widely applied in kirchhoff migration when the new wave equation is solved numerically using finite difference schemes numerical dispersion in the original wave equation is attenuated significantly leading to a much more accurate finite difference scheme with little additional computational cost numerical tests on both synthetic and field data sets in both two and three dimensions demonstrate that the optimized wave equation dramatically improves the image quality by successfully attenuating dispersive noise the adaptive application of this new wave equation only increases the computational cost slightly

a highly efficient time space domain optimized method with lax wendroff type time discretization for the scalar wave equation abstract in this paper we propose an efficient time space domain optimized optts finite difference scheme to model 2d and 3d scalar wave propagation it adopts piecewise constant interpolation coefficients for several consecutive courant number ranges which avoids the extra time costs caused by loading the coefficients consecutively according to different wave velocities in heterogeneous media the new scheme is capable of suppressing numerical dispersion errors using a large time interval because we introduce a lax wendroff type time discretization which utilizes the wave field information of o m 1 m 2 neighboring grid points in each step with merely o m 1 m 2 computation where m 1 and m 2 are the stencil radii to generate the 2nd order and 4th order spatial derivatives the improved computational efficiency and accuracy of optts are validated by substantial experiments using both theoretical analysis and numerical modeling they show that in heterogeneous models the maximal courant numbers reach 1 0 and 0 85 in 2d and 3d cases respectively without severe temporal error and the scheme is computationally nearly three times faster than its high order counterpart providing a powerful tool for large scale modeling and high resolution imaging

splitting algorithms for the high order compact finite difference schemes in wave equation modeling abstractwe have developed efficient splitting algorithms for high order compact finite difference methods to approximate second order space derivatives in general the methods high order compact finite difference schemes require the inversion of a multidiagonal matrix that is commonly less efficient to solve this problem we used ideas from splitting algorithms in one way wave equation migration that work by decomposing the multidiagonal matrix into a series of tridiagonal matrices and then subsequently solving the tridiagonal matrices this approach results in more efficient algorithms with little loss of accuracy the splitting algorithms can be implemented in three different ways our computational complexity analysis verifies that our methods can reduce the calculation burden from exponential to linear growth numerical experiments demonstrate the correctness and effectiveness of our algorithms

time domain explicit finite difference method based on the mixed domain function approximation for acoustic wave equation abstractexplicit finite difference fd methods with high accuracy and efficiency are preferred in full waveform inversion and reverse time migration the taylor series expansion te based fd methods can only obtain high accuracy on a small wavenumber zone we have developed a new explicit fd method with spatial arbitrary even order accuracy based on the mixed k wavenumber space domain function approximation for the acoustic wave equation and we derived the fd coefficients by minimizing the approximation error in a least squares ls sense the weighted pseudoinverse of mixed k space matrix is introduced into the ls optimization problem to improve the accuracy the new method has an exact temporal derivatives discretization in homogeneous media and also has higher temporal and spatial accuracy in heterogeneous media approximation errors and numerical dispersion analysis demonstrate that the new fd method has a higher numerical accuracy than conventional te based fd and te based time space domain disp

implicit finite difference simulations of seismic wave propagation we propose a new finite difference modeling method implicit both in space and in time for the scalar wave equation we use a three level implicit splitting time integration method for the temporal derivative and implicit finite difference operators of arbitrary order for the spatial derivatives both the implicit splitting time integration method and the implicit spatial finite difference operators require solving systems of linear equations we show that it is possible to merge these two sets of linear systems one from implicit temporal discretizations and the other from implicit spatial discretizations to reduce the amount of computations to develop a highly efficient and accurate seismic modeling algorithm we give the complete derivations of the implicit splitting time integration method and the implicit spatial finite difference operators and present the resulting discretized formulas for the scalar wave equation we conduct a thorough numerical analysis on grid dispersions of this new implicit

determining the optimal coefficients of the explicit finite difference scheme using the remez exchange algorithm explicit finite difference fd schemes are widely used in the seismic exploration field due to their simplicity in implementation and low computational cost however they suffer from strong artifacts caused by using coarse grids for high frequency applications the optimization of constant coefficients is popular in reducing spatial dispersions but current methods could not guarantee that the bandwidth of the tolerable dispersion error is the widest we have applied the remez exchange algorithm to optimize the constant coefficients of the explicit fd schemes for conventional and staggered grids the resulting dispersion errors are distributed alternately between the maxima and minima in the passband of the filter which is consistent with the most important equal ripple property of the error magnitude for the optimal solution according to the chebyshev criterion the remez exchange algorithm can determine the optimal coefficients of the fd method with only a few iterations and the resulting operator has a wider bandwidth compared with previous solutions it can handle arbitrary orders without the influence of local minima its computational cost for solving the objective function is comparable to that of the least squares method but its bandwidth is wider its accuracy is also higher than that of the maximum norm solved by the simulated annealing algorithm but its computational cost is much lower theoretically the equal ripple error can offer the widest bandwidth for suppressing numerical dispersions among all solutions obtained by the constant coefficient optimization in other words we can obtain a smaller error limitation than traditional methods under the same bandwidth this superiority over traditional methods is essential for reducing the total error accumulation which is helpful to avoid rapid error accumulations especially for large scale models and long term problems

maximizing the cfl number of stable time space domain explicit finite difference modeling abstract the time space domain explicit finite difference fd method numerically solves wave equation by applying fd to approximate its spatial and temporal derivatives this method always faces the stability problem i theoretically analyze stability condition of this method for the acoustic wave equation and find that the maximum courant friedrichs lewy cfl number of stable modeling depends on the maximum value of the spatial fd dispersion relation the conventional method commonly determines spatial fd coefficients by approximating the spatial fd dispersion to the exact relation within the given wavenumber area however outside this area the dispersion relation and hence the maximum cfl number is uncontrollable to make it controllable i propose to simultaneously approximate the spatial fd dispersion relation to a given function outside this area further i develop an algorithm to maximize the maximum cfl number stability analysis and modeling examples demonstrate that the proposed method has better stability than the conventional method especially when the maximum effective wavenumber frequency is small for the 2d case the conventional method performs stable simulation using a cfl number of no more than 0 707 but the new method can perform stable simulation using a large cfl number for example 1 6 4 8 and 9 0 and non long spatial fd stencils

time space domain implicit finite difference methods for modeling acoustic wave equations it was proved that the implicit spatial finite difference fd method can obtain a higher accuracy than the explicit fd by using even a smaller operator length however when only second order fd in time is used the combined fd is prone to temporal dispersion and easily becomes unstable when a relatively large time step is used the time space domain fd can suppress the temporal dispersion however because the spatial derivatives are solved explicitly the method suffers from spatial dispersion and a large spatial operator length has to be adopted we propose two effective time space domain implicit fd methods for modeling 2d and 3d acoustic wave equations the high order fd is first incorporated into the discretization for the second order temporal derivative and is combined with the implicit spatial fd the plane wave analysis method is used to derive the time space domain dispersion relations and two novel methods are proposed to determine the spatial and temporal fd coefficients in the joint time

acoustic and elastic numerical wave simulations by recursive spatial derivative operators anewschemeforthecalculationofspatialderivativeshas been developed the technique is based on recursive derivativeoperatorsthataregeneratedbyanlfitinthespectraldomain the use of recursive operators enables us to extend acousticandelasticwavesimulationstoshorterwavelengths the method is applied to the numerical solution of the 2d acousticwaveequationandtothesolutionoftheequationsof 2ddynamicelasticityinanisotropicmedium anexampleof reverse time migration of a synthetic data set shows that the numerical dispersion can be significantly reduced with respect to schemes that are based on finite differences the methodistestedforthesolutionsoftheequationsofdynamic elasticity by comparing numerical and analytic solutions to lamb sproblem

condor a new parallel constrained extension of powell s uobyqa algorithm experimental results and comparison with the dfo algorithm this paper presents an algorithmic extension of powell s uobyqa algorithm unconstrained optimization by quadratical approximation we start by summarizing the original algorithm of powell and by presenting it in a more comprehensible form thereafter we report comparative numerical results between uobyqa dfo and a parallel constrained extension of uobyqa that will be called in the paper condor constrained non linear direct parallel optimization using trust region method for high computing load function the experimental results are very encouraging and validate the approach they open wide possibilities in the field of noisy and high computing load objective functions optimization from 2 min to several days like for instance industrial shape optimization based on computation fluid dynamic codes or partial differential equations solvers finally we present a new easily comprehensible and fully stand alone implementation in c of the parallel algorithm

explicit 3 d migration using equiripple polynomial expansion and laplacian synthesis in f x explicit finite difference depth migration schemes wavefield downward extrapolation is carried out through spatial convolution using finite length filters existing methods for computing these filters are based on nonlinear least squares with a high computational cost or on taylor series expansion which is suboptimal in the 3 d case the physics of wavefield extrapolation requires 2 d extrapolation filters with circular symmetry recently mcclellan transformation has been used to design circularly symmetric extrapolation operators but this approach exhibits artifacts when the data are not spatially oversampled we describe an alternative method to take advantage of the circular symmetry the radial response of the filter is expanded as a polynomial in the laplacian which is synthesized as the sum of two 1 d second derivative filters using the laplacian rather than the mcclellan transform yields an artifact free impulse response for wavenumbers much closer to the nyquist wavenumber at the s

forward modeling by a fourier method a fourier or pseudospectral forward modeling algorithm for solving the two dimensional acoustic wave equation is presented the method utilizes a spatial numerical grid to calculate spatial derivatives by the fast fourier transform time derivatives which appear in the wave equation are calculated by second order differcncing the scheme requires fewer grid points than finite diffcrcnce methods to achieve the same accuracy it is therefore believed that the fourier method will prove more efficient than finitedifference methods especially when dealing with threedimensional models the fourier forward modeling method was tested against two problems a single layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling the numerical results agreed with both the analytic and physical model results furthermore the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account

two dimensional simulation of rayleigh waves with staggered sine cosine transforms and variable grid spacing simulation of rayleigh waves requires high accuracy and an adequate spatial sampling at the surface discrete cosine and sine transforms are used to compute spatial derivatives along the direction perpendicular to the surface of the earth unlike the standard fourier method these transforms allow nonperiodicboundaryconditionstobesatisfied inparticular the stress free conditions at the surface because simulation of surface waves requires more points per minimum wavelengthatthesurfacethansimulationofbodywaves theequispaced grid is not efficient to overcome this problem a grid compression is performed at the surface to obtain a denser spatial sampling grid size is minimal at the surface and increases with depth until reaching at a relatively shallow depth the grid points per wavelength required by the body waves the stress free boundary conditions are naturally handled by expanding the appropriate stress components in terms of the discrete sine transform the wave equation is solved in the particle velocity and stress formulation using a runge kutta time integration and the convolutional pml cpmlmethodtopreventreflectionsfromthemeshboundaries the simulations are very accurate for shallow sources andreceiversandlargeoffsets

an implicit finite difference operator for the helmholtz equation abstractwe have developed an implicit finite difference operator for the laplacian and applied it to solving the helmholtz equation for computing the seismic responses in the frequency domain this implicit operator can greatly improve the accuracy of the simulation results without adding significant extra computational cost compared with the corresponding conventional explicit finite difference scheme we achieved this by taking advantage of the inherently implicit nature of the helmholtz equation and merging together the two linear systems one from the implicit finite difference discretization of the laplacian and the other from the discretization of the helmholtz equation itself the end result of this simple yet important merging manipulation is a single linear system similar to the one resulting from the conventional explicit finite difference discretizations without involving any differentiation matrix inversions we analyzed grid dispersions of the discrete helmholtz equation to show the accura

on the iteration of a rational function computer experiments with newton s method using newton s method to look for roots of a polynomial in the complex plane amounts to iterating a certain rational function this article describes the behavior of newton iteration for cubic polynomials after a change of variables these polynomials can be parametrized by a single complex parameter and the newton transformation has a single critical point other than its fixed points at the roots of the polynomial we describe the behavior of the orbit of the free critical point as the parameter is varied the julia set points where newton s method fail to converge is also pictured these sets exhibit an unexpected stability of their gross structure while the changes in small scale structure are intricate and subtle

temporal high order staggered grid finite difference schemes for elastic wave propagation abstractthe traditional high order finite difference fd methods approximate the spatial derivatives to arbitrary even order accuracy whereas the time discretization is still of second order accuracy temporal high order fd methods can improve the accuracy in time greatly however the present methods are designed mainly based on the acoustic wave equation instead of elastic approximation we have developed two temporal high order staggered grid fd sfd schemes for modeling elastic wave propagation a new stencil containing the points on the axis and a few off axial points is introduced to approximate the spatial derivatives we derive the dispersion relations of the elastic wave equation based on the new stencil and we estimate fd coefficients by the taylor series expansion te the te based scheme can achieve 2m th order spatial and 2n th order temporal accuracy n 5 we further optimize the coefficients of fd operators using a combination of te and least squares ls the fd coefficients at the

a computer algorithm for determining the hausdorff dimension of certain fractals a fractal is a set which has nonintegral hausdorff dimension computation of the dimension directly from the definition would be very time consuming on a computer however the dimension can be computed using newton s method if there exists a self expanding map on the set this technique is applied to compute the dimension of the julia set of the quadratic mapping z z2 c for small real values of c 1 fractals and hausdorff dimension b mandelbrot 4 introduced the word fractal as a set for which the hausdorff besicovitch dimension strictly exceeds the topological dimension whereas the topological dimension of any subset of the plane is either one or two the hausdorff dimension may be nonintegral physicists 7 use the word strange in this context informally the hausdorff dimension of a subset x of a metric space can be pictured by overlaying an n by n gridwork of boxes on x for arbitrarily large values of n in this manner x is covered by n2 boxes if x is linear then only n of the boxes intersect x and x has hausdorff dimension one if x covers most of the plane then approximately n2 of the boxes intersect x and x has hausdorff dimension two if x falls between the first and second case then x intersects nd boxes for some value of d between one and two and x is a fractal with hausdorff dimension d in other words if x has dimension d then approximately nd boxes of size 1 n are needed to cover x this might be of interest when drawing x on some coarse device such as a graphics terminal where a point on the device is in reality a ball of size 1 n strictly speaking the gridwork picture describes the minkowski dimension it is equal to the hausdorff dimension in all nice cases which includes all the sets discussed in this paper more formally definition let c e be a covering on x by countably many balls bj ri iei of radius ri 0 form the sum ii ri take the infimum of the sum over all coverings c e define a function ha by taking the limit of the infimums as e approaches zero notationally this says h x lim inf erg e o kzei this is a way of measuring the area needed to cover x by small balls with the convention that a ball of radius r has area ra if af is too small then h x is infinite if af is too large then h x is zero there is a unique value where 1988 american mathematical society 0025 5718 88 1 00 25 per page 291 received september 17 1985 revised july 31 1987 1980 mathematics subject classification 1985 revision primary 58f21 30d05 this content downloaded from 207 46 13 128 on wed 07 sep 2016 05 52 01 utc all use subject to http about jstor org terms

prefactored optimized compact finite difference schemes for second spatial derivatives we have described systematically the processes of developing prefactored optimized compact schemes for second spatial derivatives first instead of emphasizing high resolution of a single monochromatic wave we focus on improving the representation of the compact finite difference schemes over a wide range of wavenumbers this leads to the development of the optimized compact schemes whose coefficients will be determined by fourier analysis and the least squares optimization in the wavenumber domain the resulted optimized compact schemes provide the maximum resolution in spatial directions for the simulation of wave propagations however solving for each spatial derivative using these compact schemes requires the inversion of a band matrix to resolve this issue we propose a prefactorization strategy that decomposes the original optimized compact scheme into forward and backward biased schemes which can be solved explicitly we achieve this by ensuring a property that the real numerical wavenumbers o

on the invariant sets of a family of quadratic maps the julia setb for the mappingz z 2 is considered where is a complex parameter for 2 a new upper bound for the hausdorff dimension is given and the monic polynomials orthogonal with respect to the equilibrium measure onb are introduced a method for calculating all of the polynomials is provided and certain identities which obtain among coefficients of the three term recurrence relations are given a unifying theme is the relationship betweenb and chains which is explored for 1 4 2 and for with 1 4 with the aid of the bottcher equation thenb is shown to be a holder continuous curve for 1 4

the application of high order differencing to the scalar wave equation the second order central difference is often used to approximate the derivatives of the wave equation it is demonstrated that gains in computational efficiency can be made by using high order approximations for these derivatives a one dimensional model is used to illustrate the relative accuracy of o t2 x2 o t2 x4 o t4 x4 ando t4 x10 central difference schemes for comparison o t2 ando t4 pseudospectral schemes are used as an additional measure of performance the results indicate that o t4 x10 differencing can achieve similar accuracy as the o t4 spectral scheme for practical illustration a two dimensional form of the o t4 x10 algorithm is used to compute the exploding reflector response of a salt dome model and compared with a fine grid o t2 x4 result transmissive sponge like boundary conditions are also examined and shown to be effective

how to calculate the hausdorff dimension using fractal structures in this paper we provide the first known overall algorithm to calculate the hausdorff dimension of any compact euclidean subset this novel approach is based on both a new discrete model of fractal dimension for a fractal structure which considers finite coverings and a theoretical result that the authors contributed previously in 14 this new procedure combines fractal techniques with tools from machine learning theory in particular we use a support vector machine to decide the value of the hausdorff dimension in addition to that we artificially generate a wide collection of examples that allows us to train our algorithm and to test its performance by external proof some analyses about the accuracy of this approach are also provided

parallel evolutionary algorithms for optimization problems in aerospace engineering abstract this paper presents the recent developments in hierarchical genetic algorithms hgas to speed up the optimization of aerodynamic shapes it first introduces hgas a particular instance of parallel gas based on the notion of interconnected sub populations evolving independently previous studies have shown the advantages of introducing a multi layered hierarchical topology in parallel gas such a topology allows the use of multiple models for optimization problems and shows that it is possible to mix fast low fidelity models for exploration and expensive high fidelity models for exploitation finally a new class of multi objective optimizers mixing hgas and nash game theory is defined these methods are tested for solving design optimization problems in aerodynamics a parallel version of this approach running a cluster of pcs demonstrate the convergence speed up on an inverse nozzle problem and a high lift problem for a multiple element airfoil

time space domain dispersion relation based finite difference method with arbitrary even order accuracy for the 2d acoustic wave equation high order finite difference fd methods have been widely used for numerical solution of acoustic wave equations it has been reported that the modeling accuracy is of 2nd order when the conventional 2m th order space domain fd and the 2nd order time domain fd stencils are directly used to solve the acoustic wave equation under the same discretization the present version of time space domain dispersion relation based fd method can improve the accuracy from 2nd order to 2m th order along eight directions for the 2d acoustic wave equation to increase the accuracy further we propose a new fd stencil for 2d acoustic wave equation modeling this new time space domain dispersion relation based fd stencil can reach the same arbitrary even order accuracy along all directions and is more accurate and more stable than the conventional one for the same m dispersion analysis and modeling examples demonstrate its advantages

globally optimal finite difference schemes based on least squares abstractspatial finite difference fd coefficients are usually determined by the taylor series expansion te or optimization methods the former can provide high accuracy on a smaller wavenumber or frequency zone and the latter can give moderate accuracy on a larger zone present optimization methods applied to calculate fd coefficients are generally gradient like or global optimization like algorithms and thus iterations are involved they are more computationally expensive and sometimes the global solution may not be found i examined second order spatial derivatives and computed the optimized spatial fd coefficients over the given wavenumber range using the least squares ls method the results indicated that the fd accuracy increased with increasing operator length and decreasing wavenumber range therefore for the given error and operator length globally optimal spatial fd coefficients can be easily obtained some optimal fd coefficients were given i developed schemes to obtain optimized ls

optimal staggered grid finite difference schemes based on the minimax approximation method with the remez algorithm abstractfinite difference fd schemes especially staggered grid fd sfd schemes have been widely implemented for wave extrapolation in numerical modeling whereas the conventional approach to compute the sfd coefficients is based on the taylor series expansion te method which leads to unignorable great errors at large wavenumbers in the solution of wave equations we have developed new optimal explicit sfd esfd and implicit sfd isfd schemes based on the minimax approximation ma method with a remez algorithm to enhance the numerical modeling accuracy starting from the wavenumber dispersion relations we derived the optimal esfd and isfd coefficients by using the ma method to construct the objective functions and solve the objective functions with the remez algorithm we adopt the ma based esfd and isfd coefficients to solve the spatial derivatives of the elastic wave equations and perform numerical modeling numerical analyses indicated that the ma based esfd and isfd schemes can overcome th

complex analytic dynamics on the riemann sphere dichotomie dynamique de fatou et julia points periodiques consequences du theoreme de montel l ensemble de julia est la fermeture de l ensemble des points periodiques repulseurs resultats classiques sur l ensemble de fatou classification de sullivan de l ensemble de fatou une condition pour le developpement sur l ensemble de julia la dynamique des polynomes l ensemble de mandelbrot et le travail de douady et hubbard le theoreme d application de riemann mesurable et la dynamique analytique

pseudo analytical finite difference elastic wave extrapolation based on the k space method abstractcost effective elastic wave modeling is the key to practical elastic reverse time migration and full waveform inversion implementations we have developed an efficient elastic pseudo analytical finite difference pafd scheme for elastic wave extrapolation the elastic pafd scheme is based on a modified pseudo spectral method k space method in which a pseudo analytical operator is used to ensure the high accuracy of elastic wave extrapolation however the k space method is motivated for a pure wave mode and thus its application in coupled first order elastic wave equations may cause the elastic pseudo analytical operators to suffer from crosstalk between the p and s wavefields the approaches presented attempt to overcome these shortcomings by introducing two improvements to achieve the goal this is done first by performing a predictor corrector strategy in first order elastic wave equations to eliminate those errors during wave extrapolation considering the massive computational cost in

acoustic and elastic modeling by optimal time space domain staggered grid finite difference schemes abstractstaggered grid finite difference sfd methods are widely used in modeling seismic wave propagation and the coefficients of finite difference fd operators can be estimated by minimizing dispersion errors using taylor series expansion te or optimization we developed novel optimal time space domain sfd schemes for acoustic and elastic wave equation modeling in our schemes a fourth order multiextreme value objective function with respect to fd coefficients was involved to yield the globally optimal solution with low computational cost we first used variable substitution to turn our optimization problem into a quadratic convex one and then used least squares ls to derive the optimal sfd coefficients by minimizing the relative error of time space domain dispersion relations over a given frequency range to ensure the robustness of our schemes a constraint condition was imposed that the dispersion error at each frequency point did not exceed a given threshold moreover the hybrid absorbin

uniform dispersion reduction schemes for the one dimensional wave equation in isotropic media finite difference fd methods for the wave equation in general suffer from numerical dispersion although fd methods based on accuracy give good dispersion at low frequencies waves tend to disperse for higher wavenumber in this work we will give a unified methodology to derive dispersion reduction fd schemes for the one dimensional wave equation and this new method can reduce dispersion error uniformly for all wavenumbers up to the nyquist stability criteria are given and stability analysis is done for each generated scheme

a simulation based evolutionary approach to lna circuit design optimization abstract in this paper we propose a simulation based evolutionary approach for designing low noise amplifier lna integrated circuits ics based on a genetic algorithm ga the levenberg marquardt lm method and a circuit simulator the simulation based evolutionary approach is developed for design optimization of lna circuits for a given lna circuit the simulation based evolutionary approach simultaneously optimizes the electrical specifications such as s 11 s 12 s 21 s 22 k factor the noise figure and the input third order intercept point in the process between simulation and optimization first of all the necessary parameters of the lna circuit for circuit simulation are loaded by solving a set of nonlinear ordinary differential equations the circuit simulator will then be performed for the circuit simulation and specification evaluation once the specification meets the aforementioned seven constraints we output the optimized parameters otherwise we activate the ga for the global optimization in the meanwhile the lm method searches the local optima according to the results of the ga we then call circuit simulator to compute and evaluate newer results until the specification is matched in numerical experiment 10 parameters of the lna circuit including device configuration and biasing condition are optimized with respect to the constraints the design of lna circuit is with 0 18 m metal oxide silicon filed effect transistors benchmark results also computationally confirm the robustness and efficiency of the proposed method this simulation based evolutionary approach in general can be applied to optimal design of other analog and radio frequency circuits we believe that this systematical approach will help ic design optimization and benefit computer aided design of wireless communication system on a chip