scholarly journals Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs

2021 ◽  
Vol 272 (1335) ◽  
Author(s):  
Stefan Geiss ◽  
Juha Ylinen
Keyword(s):  
Besov Spaces ◽  
Interpolation Method ◽  
Wiener Space ◽  
Local Times ◽  
Directional Derivatives ◽  
Content Type ◽  
Decoupling Method ◽  
Regularity Properties ◽  
Besov Regularity ◽  
Forward Diffusion

We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class of Besov spaces we introduce contains the traditional isotropic Besov spaces obtained by the real interpolation method, but also new spaces that are designed to investigate backwards stochastic differential equations (BSDEs). As examples we discuss the Besov regularity (in the sense of our spaces) of forward diffusions and local times. It is shown that among our newly introduced Besov spaces there are spaces that characterize quantitative properties of directional derivatives in the Malliavin sense without computing or accessing these Malliavin derivatives explicitly. Regarding BSDEs, we deduce regularity properties of the solution processes from the Besov regularity of the initial data, in particular upper bounds for their L p L_p -variation, where the generator might be of quadratic type and where no structural assumptions, for example in terms of a forward diffusion, are assumed. As an example we treat sub-quadratic BSDEs with unbounded terminal conditions. Among other tools, we use methods from harmonic analysis. As a by-product, we improve the asymptotic behaviour of the multiplicative constant in a generalized Fefferman inequality and verify the optimality of the bound we established.

A cell-based smoothed point interpolation method (CS-PIM) for 2D thermoelastic problems

2017 ◽  
Vol 27 (6) ◽  
pp. 1249-1265 ◽  
Author(s):  
Yijun Liu ◽  
Guiyong Zhang ◽  
Huan Lu ◽  
Zhi Zong
Keyword(s):  
Thermal Stresses ◽  
Interpolation Method ◽  
Content Type ◽  
Novel Approach ◽  
Convergence Results ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Thermoelastic Problems ◽  
Gradient Smoothing ◽  
Practical Implications

Purpose Due to the strong reliance on element quality, there exist some inherent shortcomings of the traditional finite element method (FEM). The model of FEM behaves overly stiff, and the solutions of automated generated linear elements are generally of poor accuracy about especially gradient results. The proposed cell-based smoothed point interpolation method (CS-PIM) aims to improve the results accuracy of the thermoelastic problems via properly softening the overly-stiff stiffness. Design/methodology/approach This novel approach is based on the newly developed G space and weakened weak (w2) formulation, and of which shape functions are created using the point interpolation method and the cell-based gradient smoothing operation is conducted based on the linear triangular background cells. Findings Owing to the property of softened stiffness, the present method can generally achieve better accuracy and higher convergence results (especially for the temperature gradient and thermal stress solutions) than the FEM does by using the simplest linear triangular background cells, which has been examined by extensive numerical studies. Practical implications The CS-PIM is capable of producing more accurate results of temperature gradients as well as thermal stresses with the automated generated and unstructured background cells, which make it a better candidate for solving practical thermoelastic problems. Originality/value It is the first time that the novel CS-PIM was further developed for solving thermoelastic problems, which shows its tremendous potential for practical implications.

Simulating swing dynamics of a power system model using nonlinear model order reduction

2019 ◽  
Vol 38 (6) ◽  
pp. 1918-1930
Author(s):  
Satyavir Singh ◽  
Mohammad Abid Bazaz ◽  
Shahkar Ahmad Nahvi
Keyword(s):  
Power System ◽  
System Dynamics ◽  
Interpolation Method ◽  
Computational Cost ◽  
Nonlinear Function ◽  
Computational Time ◽  
Reduced Basis ◽  
Power System Dynamics ◽  
Content Type ◽  
On Line

Purpose The purpose of this paper is to demonstrate the applicability of the Discrete Empirical Interpolation method (DEIM) for simulating the swing dynamics of benchmark power system problems. The authors demonstrate that considerable savings in computational time and resources are obtained using this methodology. Another purpose is to apply a recently developed modified DEIM strategy with a reduced on-line computational burden on this problem. Design/methodology/approach On-line computational cost of the power system dynamics problem is reduced by using DEIM, which reduces the complexity of the evaluation of the nonlinear function in the reduced model to a cost proportional to the number of reduced modes. The on-line computational cost is reduced by using an approximate snap-shot ensemble to construct the reduced basis. Findings Considerable savings in computational resources and time are obtained when DEIM is used for simulating swing dynamics. The on-line cost implications of DEIM are also reduced considerably by using approximate snapshots to construct the reduced basis. Originality/value Applicability of DEIM (with and without approximate ensemble) to a large-scale power system dynamics problem is demonstrated for the first time.

Frame Characterizations of Besov and Triebel–Lizorkin Spaces on Spaces of Homogeneous Type and their Applications

2002 ◽  
Vol 9 (3) ◽  
pp. 567-590
Author(s):  
Dachun Yang
Keyword(s):  
Besov Spaces ◽  
Interpolation Method ◽  
Real Interpolation ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Entropy Numbers ◽  
Compact Embeddings

Abstract The author first establishes the frame characterizations of Besov and Triebel–Lizorkin spaces on spaces of homogeneous type. As applications, the author then obtains some estimates of entropy numbers for the compact embeddings between Besov spaces or between Triebel–Lizorkin spaces. Moreover, some real interpolation theorems on these spaces are also established by using these frame characterizations and the abstract interpolation method.

Nonlinear dynamic analysis of multiple grooved water-lubricated journal bearings using attenuation rate interpolation method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Qiang Li ◽  
Qinglei Liu ◽  
Yujun Wang ◽  
Shuo Zhang ◽  
Yujing Du ◽  
...  
Keyword(s):  
Dynamic Analysis ◽  
Nonlinear Dynamic ◽  
Interpolation Method ◽  
Nonlinear Dynamic Analysis ◽  
Water Film ◽  
Friction Torque ◽  
Rotor Speed ◽  
Content Type ◽  
Attenuation Rate ◽  
Critical Instability

Purpose The stringent requirements for environmental protection have induced the extensive applications of water-lubricated journal bearings in marine propulsion. The nonlinear dynamic analysis of multiple grooved water-lubricated bearings (MGWJBs) has not been fully covered so far in the literature. This study aims to conduct the nonlinear dynamic analysis of the instability for MGWJBs. Design/methodology/approach An attenuation rate interpolation method is proposed for the determination of the critical instability speed. Based on a structured mesh movement algorithm, the transient hydrodynamic force model of MGWJBs is set up. Furthermore, the parameters’ analysis of nonlinear instability for MGWJBs is conducted. The minimum water film thickness, side leakage, friction torque and power loss of friction are fully analyzed. Findings With the increase of speed, the journal orbits come across the steady state equilibrium motion, sub-harmonic motion and limit circle motion successively. At the limit circle motion stage, the orbits are much larger than that of steady state equilibrium and sub-harmonic motion. The critical instability speed increases when the spiral angle decreases or the groove angle increases. The minimum water film thickness peak is at the rotor speed of 4,000 r/min for the MGWJB with Sa = 0°. As rotor speed increases, the side leakage decreases slightly while the friction torque and the power loss of friction increase gradually. Originality/value Present research provides a beneficial reference for the dynamic mechanism analysis and design of MGWJBs.

A novel hybrid meshless method for seepage flows in non-homogeneous and anisotropic soils

2018 ◽  
Vol 35 (2) ◽  
pp. 867-886
Author(s):  
Mohammad Hajiazizi ◽  
Adel Graili
Keyword(s):  
Interpolation Method ◽  
Seepage Flow ◽  
Delta Function ◽  
Sharp Corner ◽  
Content Type ◽  
Seepage Flows ◽  
Analytical Scheme ◽  
Point Interpolation Method ◽  
Singularity Point ◽  
Anisotropic Soil

Purpose The purpose of this paper is to extend the scaled boundary radial point interpolation method (SBRPIM), as a novel semi-analytical scheme, to the analysis of the steady state confined seepage flows. Design/methodology/approach This method combines the advantages of the scaled boundary finite element method and the BRPIM. In this method, only boundary nodes are used, no fundamental solution of the problem is required, and as the shape functions constructed based on the RPIM satisfy the Kronecker delta function property, the boundary conditions of problems can be imposed accurately and easily. Findings Three numerical examples, including seepage flow through homogeneous and non-homogeneous soils, are analyzed in this paper. Comparing the flow net obtained by SBRPIM and other numerical methods confirms the ability of the proposed method in analyzing seepage flows. In addition, in these examples, the accuracy of the SBRPIM in modeling the velocity singularity at a sharp corner is illustrated. SBRPIM accurately models the singularity point in non-homogeneous and anisotropic soil. Originality/value SBRPIM method is a simple effective tool for analyzing various kinds of engineering problems. It is easy to implement for modeling the velocity singularity at a sharp corner. The proposed method accurately models the singularity point in non-homogeneous and anisotropic soil.

Modifications to the SIMPLE algorithm with the MDCD approach for incompressible flow simulation

2018 ◽  
Vol 28 (9) ◽  
pp. 2208-2230 ◽  
Author(s):  
Siya Jiang ◽  
Song Fu
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Interpolation Method ◽  
Flow Simulation ◽  
Simple Algorithm ◽  
Separated Flow ◽  
Taylor Vortex ◽  
Simple Type ◽  
Content Type ◽  
Modified Algorithm

Purpose The purpose of the paper is to propose some modifications to the SIMPLE (semi-implicit method for pressure-linked equations) algorithm. These modifications can ensure the numerical robustness and optimize computational efficiency. They remarkably promote the ability of the SIMPLE algorithm for incompressible DNS (direct numerical simulation) of multiscale problems, such as transitional flows and turbulent flows, by improving the properties of dispersion and dissipation. Design/methodology/approach The MDCD (minimized dispersion and controllable dissipation) scheme and MMIM (modified momentum interpolation method) are introduced. Six typical test cases are used to validate the modified algorithm, including the linear convective flow, lid-driven cavity flow, laminar boundary layer, Taylor vortex and DHIT (decaying homogenous isotropic turbulence). Particularly, a highly unsteady DNS of separated-flow transition in turbomachinery is precisely predicted by the modified algorithm. Findings The numerical examples show the distinct superiority of the modified algorithm in both internal flows and external flows. The advantages of the MDCD scheme and MMIM make the SIMPLE algorithm a promising method for DNS. Originality/value Some effective modifications to the SIMPLE algorithm are addressed. It is the first attempt to introduce the MDCD approach into the SIMPLE-type algorithms. The new algorithm is especially suitable for the incompressible DNS of convection-dominated flows.

A fast noise-robust interpolation method based on second-order directional-derivatives

2015 ◽  
Vol 61 (3) ◽  
pp. 368-375 ◽  
Author(s):  
Seung-Jun Lee ◽  
Jong-Hwan Kim ◽  
Seok-Jae Kang ◽  
Wonhee Choe ◽  
Sung-Jea Ko
Keyword(s):  
Interpolation Method ◽  
Second Order ◽  
Directional Derivatives ◽  
Noise Robust

scholarly journals Stochastic Integrals in Abstruct Wiener Space II: Regularity Properties

1973 ◽  
Vol 50 ◽  
pp. 89-116 ◽  
Author(s):  
Hui-Hsiung Kuo
Keyword(s):  
Wiener Space ◽  
Stochastic Integrals ◽  
Abstract Wiener Space ◽  
Regularity Properties

This paper continues the study of stochastic integrals in abstract Wiener space previously given in [14]. We will present, among other things, the detailed discussion and proofs of the results announced in [16]. Let H ⊂ B be an abstract Wiener space.

Systematic approach for asset management of urban water pipeline infrastructure systems

2017 ◽  
Vol 7 (5) ◽  
pp. 506-517 ◽  
Author(s):  
Hamed Zamenian ◽  
Juyeong Choi ◽  
Seyed Amir Sadeghi ◽  
Nader Naderpajouh
Keyword(s):  
Service Life ◽  
Spatial Pattern ◽  
Asset Management ◽  
Interpolation Method ◽  
Spatial Relationship ◽  
Urban Water ◽  
Content Type ◽  
Short Service Life ◽  
Water Pipelines ◽  
Water Pipeline

Purpose The purpose of this paper is to develop a systemic approach to evaluate physical condition of water pipeline infrastructure with limited condition assessment data that can help asset managers prioritize capital investments in maintenance projects for urban water pipeline systems. Design/methodology/approach Spatial pattern analyses are conducted in this research to find the spatial pattern of the service life of pipelines. Based on the spatial relationship, the critical areas where groups of pipelines with short service life are likely to be found were located using spatial statistical analyses. A visualized platform was also developed and used to validate the implementation of the proposed approach with the case study of urban water pipeline infrastructure in a city in the Midwest region of the USA. Findings The results of the spatial pattern analyses reveal that water pipelines are spatially clustered based on their service life. Further, it was found that on average the pipelines in the center of a city have longer service life while the average expected service life of the pipelines in the marginal areas is shorter. The interpolation method produced raster data with continuous information about the service years of pipelines that are useful for asset maintenance planning. Originality/value With the limited data, the proposed approach enables identification of the critical area of water pipelines with the likelihood of shorter service life. This result can be used as a priority rule for a rehabilitation plan and contributes to shifting from a responsive to a preventive approach in underground asset management.

A robust finite volume method for three-dimensional filling simulation of plastic injection molding

2017 ◽  
Vol 34 (3) ◽  
pp. 814-831 ◽  
Author(s):  
Junjie Liang ◽  
Wan Luo ◽  
Zhigao Huang ◽  
Huamin Zhou ◽  
Yun Zhang ◽  
...  
Keyword(s):  
Finite Volume ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Phase Flow ◽  
Two Phase ◽  
Content Type ◽  
Fluid Properties ◽  
The Face ◽  
Finite Volume Approach ◽  
Plastic Injection

Purpose The purpose of this paper is to develop a finite volume approach for the simulation of three-dimensional two-phase (polymer melt and air) flow in plastic injection molding which is capable of robustly handling the mesh non-orthogonality and the discontinuities in fluid properties. Design/methodology/approach The presented numerical method is based on a cell-centered unstructured finite volume discretization with a volume-of-fluid technique for interface capturing. The over-relaxed approach is adopted to handle the non-orthogonality involved in the discretization of the face normal derivatives to enhance the robustness of the solutions on non-orthogonal meshes. A novel interpolation method for the face pressure is derived to address the numerical stability issues resulting from the density and viscosity discontinuities at the melt–air interface. Various test cases are conducted to evaluate the proposed method. Findings The presented method was shown to be satisfactorily accurate by comparing simulations with analytical and experimental results. Besides, the effectiveness of the proposed face pressure interpolation method was verified by numerical examples of a two-phase flow problem with various density and viscosity ratios. The proposed method was also successfully applied to the simulation of a practical filling case. Originality/value The proposed finite volume approach is more tolerant of non-orthogonal meshes and the discontinuities in fluid properties for two-phase flow simulation; therefore, it is valuable for engineers in engineering computations.

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