Sentence examples for use of numerical approaches from inspiring English sources

However, the resulting dimensionality increase (several thousands of spins) makes the geometric solution inapplicable, and requires the use of numerical approaches to solve the problem.

Experimental investigation of these transient events is expensive and time-consuming, and nowadays the use of numerical approaches is on the increase.

For example: the non-existence of antiderivative, the corresponding limit does not exist or integrals depending on parameters which complicate the use of numerical approaches.

This could be achieved by considering subpopulation-dependent variables { α i, ε i, η i, r i } (with i indicating the subpopulation), however preventing an analytical treatment to solve the system due to the additional complications considered, thus requiring the use of numerical approaches.

Simulations of steady-state and transient moisture flow, transient gas flow, tracer transport, and thermal loading scenarios are performed, using a variety of numerical approaches to treat fracture matrix (F M) interactions, including an effective continuum model (ECM) and several varieties of dual-continua models.

Nonetheless, most previous triple-continuum models were solved using analytical method instead of numerical approach to predict the transient pressure in the reservoir.

Several classical examples are presented to illustrate the use of this numerical approach.

The results show the potential use of this numerical approach as a design tool to optimize the forced-air cooling process of horticultural products.

Although originally designed for geomechanical applications, this study has investigated the use of this numerical approach to model WC-Co material at the mesoscale.

Improvements to both the mathematical and numerical formulations of the model have moderated the impact of linearizing the stress term; simulations with the original EVP formulation and the improved version are used to explain the consequences of using different numerical approaches.

The actuation of such device has been simulated using several numerical approaches including full determination of electrostatic potentials with accurate description of fields at the wedge region, electron beam propagation inside the device, and evaluation of the current density distributions at the anode detector screen.