... in time and space. Nonlinear solvers based on local-global, domain-decomposition strategies have proved to be significantly more robust than regular Newton but come at a higher computational cost per iteration. The chief example of one such strategy is additive Schwarz preconditioned exact Newton (ASPEN...

.... Compared to applying CPR to the reservoir matrix without well fill-in, the new method yields lower linear iteration counts, similar to those that result from applying CPR to the reservoir matrix with well fill-in (explicit Schur complement). However, each iteration is less costly since one avoids the fill...

... the optimal dissipation matrix for multiphase compositional hyperbolic systems. We assess the new nonlinear solver through multiple numerical examples. Results reveal that the damped-Newton solver suffers from serious restrictions on timestep sizes and wasted iterations. In contrast, the DBC solver provides...

... solving a nonlinear equation iteratively using a Newton-Raphson method. In each iteration, a symmetric linear system is solved by matrix factorization, e.g., either Cholesky-decomposition (CD), eigenvalue-decomposition (EVD), or singular-value-decomposition (SVD). This paper investigates the computational...

... systems. The first method applies a Picard iteration that does not require Jacobian matrix evaluations or linear solution. The second applies a modified Seidel iteration that additionally infers locality automatically. The third algorithm applies Newton's method to the preconditioned system. The solvers...

... & gas artificial intelligence node equation of state machine learning realization tolerance partition simulation jacobian producer granularity topology algorithm united states government cgnet mismatch graph iteration history matching spe reservoir simulation conference...

... case with 26 wells while varying the average reservoir permeability. We first show that the BFGS algorithm delivers promising performance as in many cases it results in the most rapid improvement for the objective-function values (especially in early iterations). Further testing results confirm...

... pressure, this new algorithm is based on the Newton iteration and line search, which guarantees a global convergence. We obtain the Newton direction by utilizing the modified Cholesky factorization to ensure a descending direction and combine line search to facilitate the iterations in the feasible domain...

... modeling & simulation algorithm preconditioner united states government artificial intelligence linear iteration num europe government iteration convergence linear solver convergence multistage preconditioner transmissibility coarse grid equation neighborhood Introduction Since...

... Newton optimization and an iterative Ensemble Smoother method for sampling the posterior distribution. We show that the proposed implementation of SVGD can capture the posterior distribution and complicated geometry. For reservoir IC Fault test problem, the method effectively samples multiple modes...

... and the in-situ fluid compositions that can exhibit temporal evolution. In many complicated scenarios, a physical critical temperature as well as saturation pressure does not exist, and the iterative sequence fails to converge. We train the classifier to identify, a-priori, if a sequence of iterations...

... computation gpu architecture architecture solver iteration preconditioner gpus gpu operation cpu test case implementation petroleum engineer kernel simulation kernel Introduction Reservoir simulation is a valuable tool used by the oil and gas industry for modeling subsurface flow...

... The mapped average number of iterations report (see. Fig. 12b ) highlights that C m a s s s focuses on high-velocity regions joining the injector with the active wells (similar to the classical CFL), while C v o l p selects the top of the domain as the free gas...

...-problems. In standard SFI, the sub-problems are usually fully solved at each outer iteration. This can result in wasted computations that contribute little towards the coupled solution. The issue is known as ‘over-solving’. Our objective is to minimize the cost while maintain or improve the convergence...

... and displacement. fracture unknown initialization where the third equation is associated with the tip failure criterion and extra unknown is Δ t . The terms R m and R flow are the residuals of mechanical and flow systems evaluated at time t n +1 . The equation system is solved iteratively until...

... combined with the Gaussian kernel (Gaussian -SVR) is utilized to construct proxies. An iterative self-adjusting process prepares the training knowledgebase to develop robust proxies and minimizes computational time. The proxies’ hyperparameters will be optimally designed using Bayesian Optimization...

... such a nonlinear system is to use Newton's method. That is, we write x = x 0 + Δ x , and use a standard multidimensional Taylor expansion to derive the iterative scheme, (5) d R d x ( x i ) δ x i = − R ( x i ) ,   x i + 1 = x i + δ x i...

... stabilized at 12 vs. 30 iterations), and a lower computational cost (150-250 vs. 1,300 runs to achieve the same NPV) over the reference methods. Similar performance improvement was also observed in another application to a North Sea type reservoir. This demonstrated the general applicability of the proposed...

... conditions) and show that with the proper implementation of physical constraints, a robust solution can be trained within a reasonable amount of time and iterations. We revisit some of the limitations presented in previous work [ 1 ] and further the applicability of this method in a forward, pure hyperbolic...

... to include a compositional description based on standard cubic equations of state. We describe the motivations for the formulation we select to make optimal use of GPU characteristics, including choice of primary variables and iteration scheme. We then describe performance results on an example sector model...