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All these will translate into a multi-objective optimization problem to be solved for each case.
This leads to a sequence of reduced order random eigenvalue problems to be solved for each eigenmode of interest.
The major computation involved in this method appears in the learning phase, where three sets of simultaneous linear equations must be solved for each observed image.
Only small systems of linear equations with the dimension of the number of nodes included in the domain of influence have to be solved for each node.
This means that, in each optimization step, a large finite element problem must be solved for each load case, leading to an enormous computational effort.
In addition, the adaptive dynamic reduced chemistry further accelerates the chemistry integration process due to less ordinary differential equations (ODEs) to be solved for each cluster.
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For each replication, a separate probabilistic traveling salesman problem (TSP) is solved for each zone.
The Newtonian equations of motion are solved for each simulated particle in the system.
The Navier equations of equilibrium are solved for each layer in the frequency domain.
A network optimization model is solved for each service leg to evaluate a number of what-if scenarios.
The corresponding stress path is solved for each experimental strain path based on Yld2000-2d yield function and Chaboche hardening law.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com