In the multi-variate case however, when two or more properties (such as size, shape, composition etc.) are introduced, the efficiency of deterministic methods suffers and stochastic particle (Monte-Carlo) methods are an attractive alternative.
In the multi-variate case however, when two or more properties (such as size, shape, composition etc.) are introduced, special approximation methods that suffer less from curse of dimensionality has to be applied. When accuracy of the solution is not of primary importance, stochastic particle (Monte-Carlo) methods are an attractive alternative.