We present a numerical algorithm to solve the Boltzmann equation for theelectron distribution function in magnetic multilayer heterostructures withnon-collinear magnetizations. The solution is based on a scattering matrixformalism for layers that are translationally invariant in plane so thatproperties only vary perpendicular to the planes. Physical quantities like spindensity, spin current, and spin-transfer torque are calculated directly fromthe distribution function. We illustrate our solution method with a systematicstudy of the spin-transfer torque in a spin valve as a function of itsgeometry. The results agree with a hybrid circuit theory developed bySlonczewski for geometries typical of those measured experimentally.
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