birational automorphism groups and the movable cone theorem for calabi yau manifolds of wehler type via universal coxeter groups thanks to the theory of coxeter groups we produce the first family of calabi yau manifolds x of arbitrary dimension n for which rm bir x is infinite and the kawamata morrison movable cone conjecture is satisfied for this family the movable cone is explicitly described it s fractal nature is related to limit sets of kleinian groups and to the apollonian gasket then we produce explicit examples of biregular automorphisms with positive entropy on some calabi yau varieties

seismic inversion based on proximal objective function optimization algorithm abstractseismic impedance inversion has become a common approach in reservoir prediction at present the critical issue in the application of seismic inversion is its low computational efficiency especially in 3d to improve the computational efficiency we have developed an inversion method derived from the proximal objective function optimization algorithm our inversion method calculates each unknown parameter in the model vector one by one during iteration compared with routine gradient dependent inversion algorithms such as the iteratively reweighted least squares irls algorithm our inversion method has lower computational complexity as well as higher efficiency in addition to obtain a sparse reflectivity series a long tailed cauchy distribution is used as the a priori constraint the weak nonlinear problem owing to the introduction of cauchy sparse constraint is addressed by taking advantage of reweighting strategy results of synthetic and real data tests illustrate that the proposed inv

a multiple level set method for 3d inversion of magnetic data abstractwe have developed a multiple level set method for inverting magnetic data produced by weak induced magnetization only the method is designed to deal with a specific class of 3d magnetic inverse problems in which the magnetic susceptibility is known and the objective of the inversion is to find the boundary or geometric shape of the causative bodies we adopt the conceptual representation of the subsurface geologic structure by a set of magnetic bodies each having a uniform magnetic susceptibility embedded in a nonmagnetic background this representation enables us to reformulate the magnetic inverse problem into a domain inverse problem for those unknown domains defining the supports of the magnetic causative bodies because each body may take on a variety of shapes and we may not know the number of bodies a priori either we use multiple level set functions to parameterize these domains so that the domain inverse problem can be further reduced to an optimization problem of multiple level set f

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

efficient 3d inversion of magnetic data via octree mesh discretization space filling curves and wavelets abstractairborne magnetic survey data sets can contain from hundreds of thousands to millions of observations and typically cover large areas the large number of measurements combined with a model mesh to accommodate the survey extent can render an inversion of these data intractable faced with this challenge we have developed a three step procedure to locally optimize the degree of model discretization and to compress the corresponding sensitivity matrix for the inversion of magnetic data the mesh optimization is achieved through the use of adaptive octree discretization the compression is achieved by first reordering the model cells using the hilbert space filling curve and then applying the one dimensional wavelet transform to the corresponding sensitivities the fractal property of the hilbert curve groups the spatially adjacent cells into algebraically adjacent positions in the reordered model mesh and thereby maximizes the number of zero or near zero coefficients in the one dimensional wavelet

black box multigrid one major problem with the multigrid method has been that each new grid configuration has required a major programming effort to develop a code that specifically handles that grid configuration such a penalty is not required for methods like sor iccg etc in these methods one need only specify the matrix problem no matter what the grid configuration in this paper we investigate such a situation for the multigrid method the end result is code boxmg in which one need only specify the logically rectangular positive definite matrix problem boxmg does everything else necessary to set up the auxilliary coarser problems to achieve a multigrid solution

compact gravity inversion we present a new criterion for the inversion of gravity data the principle employed is to minimize the volume of the causative body which is equivalent to maximizing its compactness the anomalous density distribution is obtained using an iterative technique which is numerically stable and rapidly convergent the principle can also be adapted to include modeling of gravity anomalies by single density sources the advantage of this approach is that desirable geologic characteristics are automatically incorporated into the model with a minimum of subjective judgments on the part of the interpreter the treatment of noise in the data fits naturally into the formulation of the inversion procedure the method is illustrated by the inversion of noise free and noisy data generated from a two dimensional model consisting of a regular array of identical rectangular blocks whose densities can be individually specified in every case the algorithm successfully recovers the correct density distribution from the dat

computation of moments for maxwell s equations with random interfaces via pivoted low rank approximation abstract the aim of this paper is to compute the mean field and variance of solutions to three dimensional maxwell s equations with random interfaces via shape calculus and pivoted low rank approximation based on the perturbation theory and shape calculus we characterize the statistical moments of solutions to maxwell s equations with random interfaces in terms of the perturbation magnitude via the first order shape taylor expansion in order to capture oscillations with high resolution close to the interface an adaptive finite element method using nedelec s third order edge elements of the first kind is employed to solve the deterministic maxwell s equations with the mean interface to approximate the expectation of solutions for the second moment computation an efficient low rank approximation of the pivoted cholesky decomposition is proposed to compute the two point correlation function to approximate the variance of solutions numerical experiments are presented to demonstrate our theoretical results

calabi yau hypersurfaces in products of semi ample surfaces we study calabi yau manifolds that are embedded as hypersurfaces in products of semi ample complex surfaces we classify the deformation classes of the latter and thereby achieve a classification of the calabi yau manifolds that are constructed in this way complementing the results in the existing literature we obtain the complete hodge diamond for all calabi yau hypersurfaces in products of semi ample surfaces

a multigrid method for the cahn hilliard equation with obstacle potential we present a multigrid finite element method for the deep quench obstacle cahn hilliard equation the non smooth nature of this highly nonlinear fourth order partial differential equation make this problem particularly challenging the method exhibits mesh independent convergence properties in practice for arbitrary time step sizes in addition numerical evidence shows that this behaviour extends to small values of the interfacial parameter c several numerical examples are given including comparisons with existing alternative solution methods for the cahn hilliard equation

birational geometry of hypersurfaces in products of projective spaces we study the birational properties of hypersurfaces in products of projective spaces in the case of hypersurfaces in mathbb p m times mathbb p n we describe their nef movable and effective cones and determine when they are mori dream spaces using this we give new simple examples of non mori dream spaces and analogues of mumford s example of a strictly nef line bundle which is not ample

imaging geologic surfaces by inverting gravity gradient data with depth horizons the nonuniqueness problem that occurs when inverting potential field data is well known it can however be surmounted by jointly inverting these data with independent data sets incorporating depth information and regularizing the solution the goal is to produce a geologic model that is compatible with all measured quantities does not exceed any prescribed limits and is geologically plausible to achieve this we have developed a spatially based surface inversion algorithm that solves for the geometric interface between geologic bodies the bodies are constructed from grids of rectangular prisms that have their bottom depths adjusted by the algorithm to form the inverted surface to solve large scale inversions approximations are used in the potential field calculations that allow internal matrices to be stored in sparse format with minimal loss of accuracy the impetus for the work came from the need to combine airborne gravity gradient data with depth horizons estimated from interpreted 2d seismic

3 d inversion of gravity data we present two methods for inverting surface gravity data to recover a 3 d distribution of density contrast in the first method we transform the gravity data into pseudomagnetic data via poisson s relation and carry out the inversion using a 3 d magnetic inversion algorithm in the second we invert the gravity data directly to recover a minimum structure model in both approaches the earth is modeled by using a large number of rectangular cells of constant density and the final density distribution is obtained by minimizing a model objective function subject to fitting the observed data the model objective function has the flexibility to incorporate prior information and thus the constructed model not only fits the data but also agrees with additional geophysical and geological constraints we apply a depth weighting in the objective function to counteract the natural decay of the kernels so that the inversion yields depth information applications of the algorithms to synthetic and field data produce density models representative of true structures our results have shown that the inversion of gravity data with a properly designed objective function can yield geologically meaningful information

matrix dependent multigrid homogenization for diffusion problems for problems with strongly varying or discontinuous diffusion coefficients we present a method to compute coarse scale operators and to approximately determine the effective diffusion tensor on the coarse scale level the approach is based on techniques that are used in multigrid such as matrix dependent prolongations and the construction of coarse grid operators by means of the galerkin approximation in numerical experiments we compare our multigrid homogenization method with continuous homogenization renormalization and simple averaging approaches

elimination of adaptive grid interface errors in the discrete cell centered pressure equation classical cell centered discretization of the reservoir simulation pressure equation on anh adaptive grid results in ano 1 h leading truncation error at the grid interface a new flux continuous finite volume correction is presented together with an improved version of a previously proposed correction while both corrections eliminate the leading error the new correction exhibits the best convergence rates and has the following properties the resulting matrix is in general symmetric positive definite diagonally dominant for locally isotropic spatially varying coefficients convergence too h is demonstrated and support of the standard approximation is retained ensuring a fully implicit implementation results computed by the uncorrected classical scheme and both correction schemes are compared for two phase flow simulations with multilevel dynamic local grid refinement

fast finite volume simulation of 3d electromagnetic problems with highly discontinuous coefficients we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies and the permeability permittivity and conductivity may vary significantly the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain the present article extends methods we proposed earlier for constant permeability e haber u ascher d aruliah and d oldenburg j comput phys 163 2000 pp 150 171 d aruliah u ascher e haber and d oldenburg math models methods appl sci to appear to handle also problems in which the permeability is variable and may contain significant jump discontinuities in order to address the problem of slow convergence we reformulate maxwell s equations in terms of potentials applying a helmholtz decomposition to either the electric field or the magnetic field the null space of the curl operators can then be annihilated by adding a stabilizing term using a gauge condition and thus obtaining a strongly elliptic differential operator a staggered grid finite volume discretization is subsequently applied to the reformulated pde system this scheme works well for sources of various types even in the presence of strong material discontinuities in both conductivity and permeability the resulting discrete system is amenable to fast convergence of ilu preconditioned krylov methods we test our method using several numerical examples and demonstrate its robust efficiency we also compare it to the classical yee method using similar iterative techniques for the resulting algebraic system and we show that our method is significantly faster especially for electric sources

nonlinear magnetic inversion using a random search method a robust magnetic interpretation technique is described it is based on the minimization of an objective function by a random search algorithm instead of just one estimate this algorithm yields several points in parameter space all producing objective function values below an assumed noise level the centroid of the search points is in general a better estimate than each individual search point especially when data are corrupted by noise since no derivatives are employed even nondifferentiable objective functions such as the l1 norm of residuals can be used computation of parameter covariance matrices and confidence ellipses is possible using simple formulas the usefulness of r and q mode factor analysis applied to the correlation matrix is demonstrated the r mode factor analysis can be used in parameter variance control and the q mode factor analysis provides means to find models which are extreme in some sense the technique was applied to theoretical data and to field data from three diffe

adaptive sampling of potential field data a direct approach to compressive inversion abstractcompressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem most compression approaches focus on the model domain and very few other than traditional downsampling focus on the data domain for potential field applications to further the compression in the data domain a direct and practical approach to the adaptive downsampling of potential field data for large inversion problems has been developed the approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set while preserving the signal anomalies that contain the relevant target information two major benefits arise from this form of compressive inversion first because the approach compresses the problem in the data domain it can be applied immediately without the addition of or modification to existing inversion software second as most industry software use some form of model or sensitivity compression the

fast simulation of 3d electromagnetic problems using potentials we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies the permeability is constant the conductivity may vary significantly and the range of frequencies is moderate the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain we use a potential current formulation a with a coulomb gauge the potentials a and decompose the electric field e into components in the active and null spaces of the operator we develop a finite volume discretization on a staggered grid that naturally employs harmonic averages for the conductivity at cell faces after discretization we eliminate the current and the resulting large sparse linear system of equations has a block structure that is diagonally dominant allowing an efficient solution with preconditioned krylov space methods a particularly efficient algorithm results from the combination of bicgstab and an incomplete lu decomposition we demonstrate the efficacy of our method in several numerical experiments

complex analytic quotients of algebraic g varieties it is shown that any compact semistable quotient of a normal variety by a complex reductive lie group g in the sense of heinzner and snow is a good quotient this reduces the investigation and classification of such complex analytic quotients to the corresponding questions in the algebraic category as a consequence of our main result we show that every compact space in nemirovski s class fancyscript q g has a realisation as a good quotient and that every complete algebraic variety in fancyscript q g is unirational with finitely generated cox ring and at worst rational singularities in particular every compact space in class fancyscript q t where t is an algebraic torus is a toric variety

cross gradients joint 3d inversion with applications to gravity and magnetic data we extend the cross gradient methodology for joint inversion to three dimensional environments and introduce a solution procedure based on a statistical formulation and equality constraints for structural similarity resemblance we apply the proposed solution to the joint 3d inversion of gravity and magnetic data and gauge the advantages of this new formulation on test and field data experiments combining singular value decomposition svd and other conventional regularizing constraints we determine 3d distributions of the density and magnetization with enhanced structural similarity the algorithm reduces some misleading features of the models which are introduced commonly by conventional separate inversions of gravity and magnetic data and facilitates an integrated interpretation of the models

a finite element based domain decomposition approach for plane wave 3d electromagnetic modeling we developed a novel parallel domain decomposition approach for 3d large scale electromagnetic induction modeling in the earth we used the edge based finite element method and unstructured meshes unstructured meshes were divided into sets of nonoverlapping subdomains we used the curl curl electric field equation to carry out the analysis in each subdomain the electric field was discretized by first order vector shape functions along the edges of tetrahedral elements the tangential components of the magnetic field on the interfaces of the subdomains were defined as a set of lagrange multipliers the unknown lagrange multipliers were solved from an interface problem defined on the interfaces of the subdomains with the availability of the lagrange multipliers the electric field values in each subdomain were solved independently three synthetic examples were evaluated to verify our code excellent agreement with previously published solutions was obtained synthetic examples revealed that our domain decomposition technique is scalable with respect to the number of subdomains and robust with regard to frequency and the heterogeneous distribution of material parameters i e electric conductivity electric permittivity and magnetic permeability

3 d magnetic inversion with data compression and image focusing we develop a method of 3 d magnetic anomaly inversion based on traditional tikhonov regularization theory we use a minimum support stabilizing functional to generate a sharp focused inverse image an iterative inversion process is constructed in the space of weighted model parameters that accelerates the convergence and robustness of the method the weighting functions are selected based on sensitivity analysis to speed up the computations and to decrease the size of memory required we use a compression technique based on cubic interpolation our method is designed for inversion of total magnetic anomalies assuming the anomalous field is caused by induced magnetization only the method is applied to synthetic data for typical models of magnetic anomalies and is tested on real airborne data provided by exxonmobil upstream research company

compact kahler quotients of algebraic varieties and geometric invariant theory abstract given an action of a complex reductive lie group g on a normal variety x we show that every analytically zariski open subset of x admitting an analytic hilbert quotient with projective quotient space is given as the set of semistable points with respect to some g linearised weil divisor on x applying this result to hamiltonian actions on algebraic varieties we prove that semistability with respect to a momentum map is equivalent to git semistability in the sense of mumford and hausen it follows that the number of compact momentum map quotients of a given algebraic hamiltonian g variety is finite as further corollary we derive a projectivity criterion for varieties with compact kahler quotient

a parallel geometric multigrid method for finite elements on octree meshes in this article we present a parallel geometric multigrid algorithm for solving variable coefficient elliptic partial differential equations on the unit box with dirichlet or neumann boundary conditions using highly nonuniform octree based conforming finite element discretizations our octrees are 2 1 balanced that is we allow no more than one octree level difference between octants that share a face edge or vertex we describe a parallel algorithm whose input is an arbitrary 2 1 balanced fine grid octree and whose output is a set of coarser 2 1 balanced octrees that are used in the multigrid scheme also we derive matrix free schemes for the discretized finite element operators and the intergrid transfer operations the overall scheme is second order accurate for sufficiently smooth right hand sides and material properties its complexity for nearly uniform trees is mathcal o frac n n p log frac n n p mathcal o n p log n p where n is the number of octree nodes and n p is the number of processors our implementation uses the message passing interface standard we present numerical experiments for the laplace and navier linear elasticity operators that demonstrate the scalability of our method our largest run was a highly nonuniform 8 billion unknown elasticity calculation using 32 000 processors on the teragrid system ranger at the texas advanced computing center our implementation is publically available in the dendro library which is built on top of the petsc library from argonne national laboratory

multigrid preconditioning for krylov methods for time harmonic maxwell s equations in three dimensions we consider the rapid simulation of three dimensional electromagnetic problems in geophysical parameter regimes where the conductivity may vary significantly and the range of frequencies is moderate toward developing a multigrid preconditioner we present a fourier analysis based on a finite volume discretization of a vector potential formulation of time harmonic maxwell s equations on a staggered grid in three dimensions we prove grid independent bounds on the eigenvalue and singular value ranges of the system obtained using a preconditioner based on exact inversion of the dominant diagonal blocks of the non hermitian coefficient matrix this result implies that a preconditioner that uses single multigrid cycles to effect inversion of the diagonal blocks also yields a preconditioned system with an ell 2 condition number bounded independent of the grid size we then present numerical examples for more realistic situations involving large variations in conductivity i e jump discontinuities block preconditioning with one multigrid cycle using dendy s boxmg solver is found to yield convergence in very few iterations apparently independent of the grid size the experiments show that the somewhat restrictive assumptions of the fourier analysis do not prohibit it from describing the essential local behavior of the preconditioned operator under consideration a very efficient practical solver is obtained

an octree multigrid method for quasi static maxwell s equations with highly discontinuous coefficients in this paper we develop an octree discretization for maxwell s equations in the quasi static regime we then use this discretization in order to develop a multigrid method for maxwell s equations with highly discontinuous coefficients we test our algorithms and compare it to other multilevel algorithms

hybrid finite difference integral equation solver for 3d frequency domain anisotropic electromagnetic problems the modeling of the controlled source electromagnetic csem and single well and crosswell electromagnetic em configurations requires fine gridding to take into account the 3d nature of the geometries encountered in these applications that include geological structures with complicated shapes and exhibiting large variations in conductivities such as the seafloor bathymetry the land topography and targets with complex geometries and large contrasts in conductivities such problems significantly increase the computational cost of the conventional finite difference fd approaches mainly due to the large condition numbers of the corresponding linear systems to handle these problems we employ a volume integral equation ie approach to arrive at an effective preconditioning operator for our fd solver we refer to this new hybrid algorithm as the finite difference integral equation method fdie this fdie preconditioning operator is divergence free and is based on a magnetic field formulation similar to the lippman schwinger ie method this scheme allows us to use a background elimination approach to reduce the computational domain resulting in a smaller size stiffness matrix furthermore it yields a linear system whose condition number is close to that of the conventional lippman schwinger ie approach significantly reducing the condition number of the stiffness matrix of the fd solver moreover the fd framework allows us to substitute convolution operations by the inversion of banded matrices which significantly reduces the computational cost per iteration of the hybrid method compared to the standard ie approaches also well established fd homogenization and optimal gridding algorithms make the fdie more appropriate for the discretization of strongly inhomogeneous media some numerical studies are presented to illustrate the accuracy and effectiveness of the presented solver for csem single well and crosswell em applications

a framework for the upscaling of the electrical conductivity in the quasi static maxwells equations electromagnetic simulations of complex geologic settings are computationally expensive one reason for this is the fact that a fine mesh is required to accurately discretize the electrical conductivity model of a given setting this conductivity model may vary over several orders of magnitude and these variations can occur over a large range of length scales using a very fine mesh for the discretization of this setting leads to the necessity to solve a large system of equations that is often difficult to deal with to keep the simulations computationally tractable coarse meshes are often employed for the discretization of the model such coarse meshes typically fail to capture the fine scale variations in the conductivity model resulting in inaccuracies in the predicted data in this work we introduce a framework for constructing a coarse mesh or upscaled conductivity model based on a prescribed fine mesh model rather than using analytical expressions we opt to pose upscaling as a parameter estimation problem by solving an optimization problem we obtain a coarse mesh conductivity model the optimization criterion can be tailored to the survey setting in order to produce coarse models that accurately reproduce the predicted data generated on the fine mesh this allows us to upscale arbitrary conductivity structures as well as to better understand the meaning of the upscaled quantity we use 1d and 3d examples to demonstrate that the proposed framework is able to emulate the behavior of the heterogeneity in the fine mesh conductivity model and to produce an accurate description of the desired predicted data obtained by using a coarse mesh in the simulation process

toward an h independent algebraic multigrid method for maxwell s equations we propose a new algebraic multigrid amg method for solving the eddy current approximations to maxwell s equations this amg method has its roots in an algorithm proposed by reitzinger and schoberl the main focus in the reitzinger and schoberl method is to maintain null space properties of the weak nabla times nabla times operator on coarse grids while these null space properties are critical they are not enough to guarantee h independent convergence rates of the overall multigrid scheme we present a new strategy for choosing intergrid transfers that not only maintains the important null space properties on coarse grids but also yields significantly improved multigrid convergence rates this improvement is related to those we explored in a previous paper but is fundamentally simpler easier to compute and performs better with respect to both multigrid operator complexity and convergence rates the new strategy builds on ideas in smoothed aggregation to improve the approximation property of an existing interpolation operator by carefully choosing the smoothing operators we show how it is sometimes possible to achieve h independent convergence rates with a modest increase in multigrid operator complexity though this ideal case is not always possible the overall algorithm performs significantly better than the original scheme in both iterations and run time finally the reitzinger and schoberl method as well as our previous smoothed method are shown to be special cases of this new algorithm

a second order discretization of maxwell s equations in the quasi static regime on octree grids in this study we consider adaptive mesh refinement for the solution of maxwell s equations in the quasi static or diffusion regime we propose a new finite volume octree discretization for the problem and show how to construct second order stencils on yee grids extending the known first order discretization stencils we then develop an effective preconditioner to the problem we show that our preconditioner performs well for discontinuous conductivities as well as for a wide range of frequencies

an alternating direction algorithm for total variation reconstruction of distributed parameters augmented lagrangian variational formulations and alternating optimization have been adopted to solve distributed parameter estimation problems the alternating direction method of multipliers admm is one of such formulations optimization methods very recently the number of applications of the admm or variants of it to solve inverse problems in image and signal processing has increased at an exponential rate the reason for this interest is that admm decomposes a difficult optimization problem into a sequence of much simpler problems in this paper we use the admm to reconstruct piecewise smooth distributed parameters of elliptical partial differential equations from noisy and linear blurred observations of the underlying field the distributed parameters are estimated by solving an inverse problem with total variation tv regularization the proposed instance of the admm solves in each iteration an and a decoupled optimization problems an operator splitting is used to simplify the treatment of the tv regularizer avoiding its smooth approximation and yielding a simple yet effective admm reconstruction method compared with previously proposed approaches the competitiveness of the proposed method with respect to the state of the art is illustrated in simulated 1 d and 2 d elliptical equation problems which are representative of many real applications

complete intersection calabi yau manifolds with respect to homogeneous vector bundles on grassmannians based on the method by kuchle math z 218 4 563 575 1995 we give a procedure to list up all complete intersection calabi yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on grassmannians for each dimension in particular we give a classification of such calabi yau 3 folds and determine their topological invariants we also give alternative descriptions for some of them

a rapid method for three dimensional modeling of magnetic anomalies a computer program has been developed for three dimensional analysis of total field magnetic anomalies due to arbitrary polarization suitable for present day personal computers a vertical sided prism with arbitrary polarization is used as a basic model a nonlinear optimization technique based on marquardt s algorithm is used to estimate all parameters of the model a combination of prisms is used to analyze more complex magnetic fields analytical methods are used to estimate the derivatives required in the simultaneous solutions of the normal equations methods have been developed to minimize the computing time in forward calculation as well as in inversion approximate equations have been derived for rapid calculation of magnetic anomalies and partial derivatives of anomalies of prismatic bodies which are valid beyond short distances from the sources the algorithm has been developed in such a way that the use of the exact and approximate equations may be efficiently monitored as a trade off between

the equivalent data concept applied to the interpolation of potential field data the equivalent layer calculation becomes more efficient by first converting the observed potential data set to a much smaller equivalent data set thus saving considerable cpu time this makes the equivalent source method of data interpolation very competitive with other traditional gridding techniques that ignore the fact that potential anomalies are harmonic functions the equivalent data set is obtained by using a least squares iterative algorithm at each iteration that solves an underdetermined system fitting all observations selected from previous iterations and the observation with the greatest residual in the preceding iteration the residuals are obtained by computing a set of predicted observations using the estimated parameters at the current iteration and subtracting them from the observations the use of cholesky s decomposition to implement the algorithm leads to an efficient solution update everytime a new datum is processed in addition when applied to interpolation problems using equiva

mimetic finite difference methods for diffusion equations on non orthogonal non conformal meshes mimetic discretizations based on the support operators methodology are derived for non orthogonal locally refined quadrilateral meshes the second order convergence rate on non smooth meshes is verified with numerical examples

mimetic discretizations for maxwell s equations we have constructed reliable finite difference methods for approximating the solution to maxwell s equations using accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus in discrete form the numerical approximation does not have spurious modes and mimics many fundamental properties of the underlying physical problem including conservation laws symmetries in the solution and the nondivergence of particular vector fields numerical examples demonstrate the high quality of the method when the medium is strongly discontinuous and for nonorthogonal nonsmooth computational grids

an algebraic multigrid approach based on a compatible gauge reformulation of maxwell s equations with the rise in popularity of compatible finite element finite difference and finite volume discretizations for the time domain eddy current equations there has been a corresponding need for fast solvers of the resulting linear algebraic systems however the traits that make compatible discretizations a preferred choice for the maxwell s equations also render these linear systems essentially intractable by truly black box techniques we propose an algebraic reformulation of the discrete eddy current equations along with a new algebraic multigrid amg technique for this reformulated problem the reformulation process takes advantage of a discrete hodge decomposition on cochains to replace the discrete eddy current equations by an equivalent 2 times2 block linear system whose diagonal blocks are discrete hodge laplace operators acting on 1 cochains and 0 cochains respectively while this new amg technique requires somewhat specialized treatment on the finest mesh the coarser meshes can be handled using standard methods for laplace type problems our new amg method is applicable to a wide range of compatible methods on structured and unstructured grids including edge finite elements mimetic finite differences covolume methods and yee like schemes we illustrate the new technique using edge elements in the context of smoothed aggregation amg and present computational results for problems in both two and three dimensions