Shifted Sobol points and multigrid Monte Carlo simulation

Multidimensional integrals arise in many problems of physics. For example, moments of the distribution function in the problems of transport of various particles (photons, neutrons, etc.) are 6-dimensional integrals. When calculating the coefficients of electrical conductivity and thermal conductivity, scattering integrals arise, the dimension of which is equal to 12. There are also problems with a significantly large number of variables. The Monte Carlo method is the most effective method for calculating integrals of such a high multiplicity. However, the efficiency of this method strongly depends on the choice of a sequence that simulates a set of random numbers. A large number of pseudo-random number generators are described in the literature. Their quality is checked using a battery of formal tests. However, the simplest visual analysis shows that passing such tests does not guarantee good uniformity of these sequences. The magic Sobol points are the most effective for calculating multidimensional integrals. In this paper, an improvement of these sequences is proposed: the shifted magic Sobol points that provide better uniformity of points distribution in a multidimensional cube. This significantly increases the cubature accuracy. A significant difficulty of the Monte Carlo method is a posteriori confirmation of the actual accuracy. In this paper, we propose a multigrid algorithm that allows one to find the grid value of the integral simultaneously with a statistically reliable accuracy estimate. Previously, such estimates were unknown. Calculations of representative test integrals with a high actual dimension up to 16 are carried out. The multidimensional Weierstrass function, which has no derivative at any point, is chosen as the integrand function. These calculations convincingly show the advantages of the proposed methods.

Research on Earthwork Calculation Based on TIN Model

In actual engineering construction, the calculation of earthwork directly affects the cost budget of the project and the selection of the optimal plan. Therefore, the calculation accuracy and efficiency of the earthwork are very important. This article introduces the construction principle of the TIN model. Based on the TIN model, the earthwork calculation is carried out by the triangular prism method. The data of a fill-excavation balance project in a rugged mountainous area is selected, and under different conditions, the TIN network method and the square grid method are used to calculate the earthwork, and the results are compared and analyzed with accuracy. Estimate. After comparative analysis, it is found that the earthwork calculation using the TIN network method is simple and cheap, and the calculation result is more accurate. It is better than the traditional square grid method as a whole, and can be used in the actual engineering earthwork calculation.

Determination of gas-saturated oil density at reservoir conditions and development of quality control index of PVT laboratory report

The oil density at the bubble point is an important thermodynamic property required in reservoir simulation and production engineering. A higher-accuracy estimate of this property would improve the accuracy of reservoir and production engineering calculations. The bubble point oil density is obtained either from separator tests of reservoir fluids or from differential gas liberation tests. A new procedure utilizing separator and differential tests is proposed whereby the experimental data yield a unique value with high accuracy for the bubble point oil density. A consistent correction of other PVT properties, which are influenced by the bubble point oil density, is required to reflect the unique density value. A quantitative quality control index is defined to measure the quality of PVT laboratory reports. This is achieved by utilizing the unique property of the bubble point oil density, which is usually ignored.

The Boundary Effect in the Accuracy Estimate for the Grid Solution of the Fractional Differential Equation

A grid method for solving the first boundary value problem for ordinary and partial differential equations with the Riemann–Liouville fractional derivative is justified. The algorithm is based on using Green’s function, the Fredholm integral equation, and the Lagrange interpolation polynomial. The impact of the Dirichlet boundary condition on the accuracy of the approximate solution is revealed and quantitatively described through the weight assessment. All the estimates provide clear evidence that the accuracy order of the grid method is higher near the boundary of the domain than it is in the inner nodes of the mesh set.

GF-7 IMAGING SIMULATION AND DSM ACCURACY ESTIMATE

GF-7 satellite is a two-line-array stereo imaging satellite for surveying and mapping which will be launched in 2018. Its resolution is about 0.8 meter at subastral point corresponding to a 20 km width of cloth, and the viewing angle of its forward and backward cameras are 5 and 26 degrees. This paper proposed the imaging simulation method of GF-7 stereo images. WorldView-2 stereo images were used as basic data for simulation. That is, we didn’t use DSM and DOM as basic data (we call it “ortho-to-stereo” method) but used a “stereo-to-stereo” method, which will be better to reflect the difference of geometry and radiation in different looking angle. The shortage is that geometric error will be caused by two factors, one is different looking angles between basic image and simulated image, another is not very accurate or no ground reference data. We generated DSM by WorldView-2 stereo images. The WorldView-2 DSM was not only used as reference DSM to estimate the accuracy of DSM generated by simulated GF-7 stereo images, but also used as “ground truth” to establish the relationship between WorldView-2 image point and simulated image point. Static MTF was simulated on the instantaneous focal plane “image” by filtering. SNR was simulated in the electronic sense, that is, digital value of WorldView-2 image point was converted to radiation brightness and used as radiation brightness of simulated GF-7 camera. This radiation brightness will be converted to electronic number n according to physical parameters of GF-7 camera. The noise electronic number n1 will be a random number between -√n and √n. The overall electronic number obtained by TDI CCD will add and converted to digital value of simulated GF-7 image. Sinusoidal curves with different amplitude, frequency and initial phase were used as attitude curves. Geometric installation errors of CCD tiles were also simulated considering the rotation and translation factors. An accuracy estimate was made for DSM generated from simulated images.