# Can we apply time-parallel methods in case of peridynamics?

Can we solve peridynamics in parallel for time-dimension using methods like MGRIT? This method can be applied for time dependent PDEs, however, since peridynamics is a non-local approach, can this method be useful here? Any help will be great.

• What is your doubt why the two could not be combined? – Wolfgang Bangerth Jul 15 at 17:19
• I am using XBraid for this cause and since peridynamics don't come to the usual ODE form u'(t)=f(u,t) I was wondering if the parallel in time idea can work here as well.If you have an idea about it maybe we can discuss it further. – spyros Jul 15 at 20:25
• After spatial discretization, every time dependent PDE becomes sort of an ODE problem, e.g. $u_t - u_{xx} = 0$ is $\vec{u}_t = A\vec{u}$ where $A$ is the discrete form of the operator $\vec{u}$ is the discrete form of the function $u$. So why not? – Abdullah Ali Sivas Jul 15 at 22:42
• The Peridynamics equation is ρ(dv/dt)=Σf(u)+b (1) where v is the velocity and f internal force density based on u. My thought was to bring (1) to the form of vi+1=Φvi+gi by using an explicit scheme vi+1=(Σf(ui)+bi)dt+vi (2).I apply MGRIT on (2) while also I update ui+1=dtvi+ui.So I don’t know if this thought can work with XBraid – spyros Jul 16 at 9:33