Pulse Spectrum Technique Research Articles

History Matching for Multiphase Reservoir Models On Shared Memory Supercomputers

A parallel algorithm using the generalized pulse spec trum technique and multilevel grid method for solving reservoir structural parameter identification problems is discussed here. The algorithm can be used to iden tify the reservoir's absolute permeability distributions by matching the computed pressure values with mea sured historical pressure values obtained at observa tion wells (history matching). Use of a multilevel grid improves the quality of the identified permeability dis tributions significantly. The whole parameter identifica tion process is very computationally intensive since a group of coupled nonlinear partial differential equa tions (PDEs) and a regularized least square problem must be solved repeatedly with different parameter values. Several hundred megabyte memory is required for reservoir models involving thousands of grid points. The block SOR scheme with red and black or dering and a parallel Householder transformation scheme were used to solve the algebraic equations resulting from the discretization of the PDEs. High speedup has been achieved by exploring parallefisnl, refining the whole program, rather than just the hot- spots, and utilizing the high-speed cache memory effi ciently.

An efficient numerical method for exterior and interior inverse problems of Helmholtz equation

The generalized pulse-spectrum technique (GPST), an efficient and versatile inversion algorithm, is used with adaptive grids to solve both exterior (scattering) and interior (cavity) boundary-shape inverse problems of two-dimensional Helmholtz equation. Numerical simulations of nontrivial examples are carried out to test the feasibility and to study the general characteristics of GPST without the real measurement data. It is found that GPST does efficiently produce very good results.

Heirarchical multigrid strategy for efficiency improvement of the GPST inversion algorithm

The efficiency of the Generalized Pulse-Spectrum Technique (GPST) inversion algorithm is further improved by the introduction of a hierarchical multigrid strategy in combination with the existing re-structuralization of algorithm. This hierarchical multigrid strategy for solving inverse problems of partial differential equations (PDEs) has nothing in common with the standard multigrid algorithms for solving direct problems of PDEs except that in both cases multiple grids are utilized. Here it is used to solve one-parameter inverse problems of two-dimensional linear evolutional partial differential equations. A simple computational complexity analysis, based upon the floating point arithmetic operation (FLO) count, has been performed. It is found that the FLO count per iteration for this new scheme is of the same order as that for solving the direct problem of the corresponding PDE. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this hierarchical multigrid strategy with algorithm re-structuralization. Indeed, this new computational scheme makes the GPST inversion algorithm much more efficient.

Generalized Pulse—Spectrum Technique for Solving Inverse Problems in Microwave Heating

ABSTRACTThe Generalized Pulse—Spectrum Technique (GPST), a versatile, efficient and stable Newton-like iterative numerical inversion algorithm with Tikhonov regularization. GPSThas been been successfully applied to many practical inverse problems, including the inverse problems of equations of the diffusion type. Methodology in applying GPST for solving the inverse problems in microwave heating of ceramic samples is described.

Generalized pulse-spectrum technique for 2-D and 2-phase history matching

The generalized pulse-spectrum technique (GPST) is a versatile and efficient Newton-like iterative algorithm for solving multiparameter inverse problems of a system of nonlinear partial differential equations. Here it is extended to perform history matching for 2-D, 2-phase, slightly compressible and immiscible simulator models, i.e., to determine the unknown reservoir parameter, permeability, from the pressure and/or saturation measurements at sparsely located observation wells. Numerical simulations of nontrivial examples are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement data. It is found that GPST inversion algorithm does give very good results.

Parallelism by hierarchy of GPST inversion algorithm for elastic wave equation

The Generalized Pulse-Spectrum Technique (GPST) is a versatile and efficient iterative numerical algorithm for solving multi-parameter inverse problems of a system of nonlinear partial differential equations. Here parallelism is introduced into the hierarchy of GPST to further improve its efficiency for solving the multi-parameter inverse problems with a large number of unknown parameters in some geophysical applications. Its implementation is quite easy and it achieves large speedup with almost no communication overhead even on a single-processor computer. Effectively, this parallelism in GPST reduces the computational effort for solving any multi-parameter inverse problem approximately to that of the corresponding single-parameter inverse problem. A simple computational complexity analysis is performed for the parallel structured GPST to estimate its speedup. At the present, the feasibility and capability of the parallel structure GPST are only tested in a limited sense by performing numerical simulations for a three-parameter and two-dimensional inverse problem of the isotropic linear elastic wave equation on a single-processor computer sequentially. It is found that the parallel structured GPST is not only as robust as the standard GPST but also shows a speedup per iteration close to its estimated value.

High level parallelism in hierarchy of GPST algorithm for parameter identification in engineering mechanics

The Generalized Pulse-Spectrum Technique (GPST) is a versatile and efficient iterative numerical algorithm for solving multi-parameter idenitification problems in engineering which can be formulated mathematically as multi-parameter inverse problems of a system of partial differential equations. Here high level parallelism is introduced into the hierarchy of GPST. By using a simple computational complexity analysis, it is shown that very large speedup with no communication overhead can be achieved even without the introduction of low level parallelism into the hierarchy of GPST. Moreover, the parallel structured GPST can achieve considerable speedup over the standard GPST even on a single-processor computer.

Convergence of a generalized pulse-spectrum technique (GPST) for inverse problems of 1-D diffusion equations in space-time domain

The problem of convergence of a special form of the generalized pulse-spectrum technique (GPST) for solving inverse problems of one-dimensional diffusion equations in space-time domain is considered. Under the assumptions that a Tikhonov regularized solution exists and the derivative operator of the regularized forward problem at the regularized solution is invertible, the iterative solutions of this special GPST converge to the Tikhonov regularized solution in C norm if the initial guess is close enough to the Tikhonov regularized solution and the rate of convergence is at least linear.

Efficiency improvement of GPST inversion algorithm

To demonstrate the possibility of improving the efficiency of the generalized pulse-spectrum technique (GPST) inversion algorithm by implementing special re-structuralization and high level parallelism into the system of discretized Fredholm integral equations of the first kind, a simple two-parameter inverse problem of two-dimensional linear evolution equation is considered. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the improved GPST without real measurement data. It is found that the improved GPST is not only as robust as the standard GPST but also, possessing the speedup, very close to the estimated one by performing the computational complexity analysis based upon FLO count.

A Generalized Pulse-Spectrum Technique (GPST) for Determining Time-Dependent Coefficients of One-Dimensional Diffusion Equations

The applicability of the generalized pulse-spectrum technique (GPST) is demonstrated for the solutions of inverse problems of one-dimensional linear diffusion equations with time-dependent coefficients. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without real measurement data. It is found that the GPST also gives excellent results and is as robust as it is for solving the time-independent coefficient inverse problems.

An iterative method for simultaneous determination of bulk and shear moduli and density variations

The Pulse-Spectrum Technique (PST), an iterative numerical method, is extended to solve the three-parameter inverse problems of two-dimensional and three-dimensional linear elastic wave equations, i.e., to determine simultaneously two-dimensional and three-dimensional bulk and shear moduli and density variations from surface data. Numerical simulations of simple but non-trivial examples are carried out on coarse computational grids to test the feasibility and to study the general characteristics of PST without the real measurement data. It is found that PST under these conditions does give reasonably good results. Moreover, a comprehensive discussion of the numerical results, their implication in actual implementing of PST, and the future improvement on PST to attend higher resolution with little additional computing costs is given.

Inverse problems for elastic plates with variable flexural rigidity

The pulse-spectrum technique (PST), an iterative numerical algorithm, is extended and further developed to solve inverse problems in the dynamic structural identification and the dynamic structural design based on the two-dimensional elastic plate model with variable flexural rigidity. Numerical simulations on several simple examples are carried out to test the feasibility and to study the general characteristics of PST without the real measurement data for the case of dynamic structural identification or with the prescribed design data for the case of dynamic structural design. It is found that PST does give satisfactory results and also fares very well in regard to the given four practical criteria for evaluating numerical methods.

A modified pulse-spectrum technique for solving inverse problems of two-dimensional elastic wave equation

The Pulse-Spectrum Technique (PST), an iterative numerical algorithm for solving multi-parameter inverse problems of partial differential equations, is modified by using the Garlerkin method to solve the Fredholm integral equation of the first kind in each iteration. In this way, the computation of the complicated Green's matrix in the integrand can be avoided. Details are presented for simultaneous determination of bulk and shear moduli and density variation of the two-dimensional elastic wave equation. Numerical simulation is carried out for an example in the geophysical prospecting to test the feasibility and to study the intrinsic characteristics of the modified PST (MPST) without the real measurement data. It is shown that MPST does give excellent results.

An Iterative Algorithm for Solving Inverse Problems of Two-Dimensional Diffusion Equations

The applicability of the iterative numerical algorithm of the pulse-spectrum technique (PST) to solve inverse problems of two-dimensional linear diffusion equations is demonstrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement data. It is found that PST also gives excellent results and is as robust as for solving the inverse problem of the one-dimensional linear diffusion equation.

A NUMERICAL METHOD FOR SIMULTANEOUS DETERMINATION OF BULK MODULUS, SHEAR MODULUS AND DENSITY VARIATIONS FOR NONDESTRUCTIVE EVALUATION

Abstract Pulse-Spectrum Technique (PST), a versatile numerical method capable of simultaneous determination of bulk and shear moduli and density variations in two-dimensional and three-dimensional test specimens with complex geometries, is developed for nondestructive evaluation. Numerical simulations are carried out to test the feasibility and to study the general characteristics of PST.

An iterative numerical algorithm for solving multi-parameter inverse problems of evolutional partial differential equations

The iterative numerical algorithm of the pulse-spectrum technique (PST) is extended and developed to solve the multi-parameter inverse problems of one-dimensional evolutional partial differential equations (wave equations or diffusion equations). It has the practical advantages of universality, economy of programing, economy of data acquisition, and economy of computing costs. Without the real measurement data, numerical simulations are carried out only for the two-parameter inverse problems of a one-dimensional linear wave equation to test the feasibility and to study the general characteristics of the PST. It is found that the PST does give excellent results and it is as robust as in the single parameter case.

An Iterative Method for Solving Inverse Problems of a Nonlinear Wave Equation

The iterative numerical algorithm of the pulse-spectrum technique (PST) is extended to solve the inverse problem for a nonlinear wave equation arising from remote sensing of the ocean sound velocity profile by using finite-amplitude acoustic waves. Its applicability is demonstrated for the one-dimensional case. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without real measurement data. It is found that the PST does give reasonably good results, and hence it is a viable method.

An iterative algorithm for solving inverse problems in structural dynamics

AbstractThe pulse‐spectrum technique (PST), an iterative numerical algorithm, is presented and extended to solve the inverse problems arising from the dynamic structural identification and structural design problems. A simple one‐dimensional shear beam model is used to demonstrate the applicability of PST. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement and design data. It is found that the PST is not only quite robust in providing accurate results but also an excellent numerical method according to the four practical criteria for evaluating numerical methods.

A numerical algorithm for solving inverse problems of two-dimensional wave equations

The new iterative numerical algorithm of the pulse-spectrum technique (PST) is extended and developed to solve inverse problems of two-dimensional linear wave equations. It has the practical advantages of having the necessary data measured on a portion of the boundary only and no geometric limitation on the testing objects. Numerical simulations on several simple examples are carried out to test the feasibility and to study the general characteristics of this technique without the real measurement data. It is found that PST does give excellent results even with a very coarse computational grid and it is as robust as in the one-dimensional case.

A pulse‐spectrum technique for remote sensing of stratified media

The applicability of the new iterative numerical algorithm of the pulse‐spectrum technique (PST) to remote sensing of the electric permittivity of a stratified medium is demonstrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of this numerical algorithm without the real measurement data. These numerical results are compared with those obtained by the spectral domain method (SDM) favorably. The effects of the initial guess and the contaminating instrument noise on the accuracy and the efficiency of numerical computation are investigated. Furthermore, it is shown by numerical simulations that this particular numerical algorithm can be applied to SDM as well as to PST.