Ali Rezaei

Ali Rezaei, Fahd Siddiqui, Giorgio Bornia et al.

In this study, a fast multipole method (FMM) is used to decrease the computational time of a fully-coupled poroelastic hydraulic fracture model with a controllable effect on its accuracy. The hydraulic fracture model is based on the poroelastic formulation of the displacement discontinuity method (DDM) which is a special formulation of the boundary element method (BEM). DDM is a powerful and efficient method for problems involving fractures. However, this method becomes slow as the number of temporal, or spatial elements increases, or necessary details such as poroelasticity, that makes the solution history-dependent, are added to the model. FMM is a technique to expedite matrix-vector multiplications within a controllable error without forming the matrix explicitly. Fully-coupled poroelastic formulation of DDM involves the multiplication of a dense matrix with a vector in several places. A crucial modification to DDM is suggested in two places in the algorithm to leverage the speed efficiency of FMM for carrying out these multiplications. The first modification is in the time-marching scheme, which accounts for the solution of previous time steps to compute the current time step. The second modification is in the generalized minimal residual method (GMRES) to iteratively solve for the problem unknowns. Several examples are provided to show the efficiency of the proposed approach in problems with large degrees of freedom (in time and space). Examples include hydraulic fracturing of a horizontal well and randomly distributed pressurized fractures at different orientations with respect to horizontal stresses. The results are compared to the conventional DDM in terms of computational processing time and accuracy. Accordingly, the proposed algorithm may be used for fracture propagation studies while substantially reducing the processing time with a controllable error.

Preslav Aleksandrov, Ali Rezaei, Nikolas Xeni et al.

This work describes a novel simulation approach that combines machine learning and device modelling simulations. The device simulations are based on the quantum mechanical non-equilibrium Greens function (NEGF) approach and the machine learning method is an extension to a convolutional generative network. We have named our new simulation approach ML-NEGF and we have implemented it in our in-house simulator called NESS (nano-electronics simulations software). The reported results demonstrate the improved convergence speed of the ML-NEGF method in comparison to the standard NEGF approach. The trained ML model effectively learns the underlying physics of nano-sheet transistor behaviour, resulting in faster convergence of the coupled Poisson-NEGF simulations. Quantitatively, our ML- NEGF approach achieves an average convergence acceleration of 60%, substantially reducing the computational time while maintaining the same accuracy.