Numerical solution of stochastic differential equations on Supercomputers

Numerical analysis of stochastic oscillators on supercomputers

“…With the initial b (0) 11 and b (1) 11 chosen in (10), the sum (11) does not have terms with odd numbers. Figure 1 shows cos(ωnh) and a (n) 11 for h = 10 −2 and ω = 2π.…”

“…It should be noted that the use of some time-consuming methods that are more accurate than the Euler method, for instance, the Milstein method [10], does not speed up solving the problem, but, on the contrary, makes it more difficult. Some preliminary investigations of the authors on solving SDEs with increasing variance on supercomputers are described in [11].…”

Simulation of the linear mechanical oscillator on GPU

“…It should be noted that the use of some time-consuming methods that are more accurate than the Euler method, for instance, the Milstein method [10], does not speed up solving the problem, but, on the contrary, makes it more difficult. Some preliminary investigations of the authors on solving SDEs with increasing variance on supercomputers are described in [21]. In this paper we study equation of linear mechanical oscillator with constant coefficients:…”

Stochastic first passage time accelerated with CUDA

“…Which value of the block to use is simply indexed by a modulo operation (line 11). At the beginning, and at each time they are employed (line 12 of Algorithm 1), a new block of values is computed from the previous one (lines [13][14][15][16][17][18][19][20] γ0 ← 0, initial normalized bias current 3: pos ← cuda.grid (1) 4:…”

“…Our purpose is to device an efficient parallel algorithms that assigns a new job to the processor as soon as it has terminated its task, and to show how this can be efficiently done on a GPU in a CUDA environment. There is a huge literature for parallel solution of stochastic differential equations where an arrival time is to be calculated, see for instance [20] and references therein. The main point is that the performances are strongly related to the communication time, and hence to the processor architecture.…”