[COPS] add PDE instances #3
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| include("shapes/circle.jl") | ||
| include("shapes/circle_rec.jl") | ||
| include("shapes/rectangle.jl") | ||
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| struct PDEProblem | ||
| a::Float64 | ||
| b::Vector{Float64} | ||
| c::Vector{Float64} | ||
| d::Vector{Float64} | ||
| p::Vector{Float64} | ||
| end | ||
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| struct PDEDiscretizationDomain | ||
| NODES::Int | ||
| ELEM::Int | ||
| DIMEN::Int | ||
| BREAK::Int | ||
| AREA::Vector{Float64} | ||
| TRIANG::Matrix{Int} | ||
| COORDS::Matrix{Float64} | ||
| BNDRY::Vector{Int} | ||
| EDGE::Array{Float64, 3} | ||
| US::Vector{Float64} | ||
| UE::Vector{Float64} | ||
| end | ||
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| function PDEDiscretizationDomain(nh, domain::Dict) | ||
| NODES = domain[:NODES] | ||
| ELEMS = domain[:ELEMS] | ||
| COORDS = domain[:COORDS] | ||
| ELEMS = domain[:ELEMS] | ||
| BNDRY = domain[:BNDRY] | ||
| DIMEN = 2 | ||
| BREAK = nh | ||
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| # Description of triangular elements | ||
| TRIANG = domain[:TRIANG] | ||
| # Edge lengths | ||
| EDGE = [ | ||
| COORDS[TRIANG[e, mod(d1, DIMEN+1)+1], d2] - COORDS[TRIANG[e, d1], d2] | ||
| for e in 1:ELEMS, d1 in 1:DIMEN+1, d2 in 1:DIMEN | ||
| ] | ||
| # Area of element | ||
| AREA = [(EDGE[e, 1, 1]*EDGE[e, 2, 2] - EDGE[e, 1, 2]*EDGE[e, 2, 1]) / 2.0 for e in 1:ELEMS] | ||
| US = domain[:US] # starting point | ||
| UE = domain[:UE] # ending point | ||
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| return PDEDiscretizationDomain( | ||
| NODES, ELEMS, DIMEN, BREAK, | ||
| AREA, TRIANG, COORDS, BNDRY, EDGE, US, UE, | ||
| ) | ||
| end | ||
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| function _update_values!(integral, energy, u, problem::PDEProblem, dom::PDEDiscretizationDomain) | ||
| # Unpack values | ||
| a, b, c, d, p = problem.a, problem.b, problem.c, problem.d, problem.p | ||
| TRIANG, EDGE = dom.TRIANG, dom.EDGE | ||
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| for b1 in 1:dom.BREAK+2, e1 in 1:dom.ELEM | ||
| integral[b1, e1] = | ||
| dom.AREA[e1]*( | ||
| 1 / (dom.DIMEN+1) * | ||
| (sum((b[TRIANG[e1,c1]]*u[b1,TRIANG[e1,c1]]^2/2- | ||
| c[TRIANG[e1,c1]]*u[b1,TRIANG[e1,c1]]^(p[TRIANG[e1,c1]]+1)/(p[TRIANG[e1,c1]]+1)+ | ||
| d[TRIANG[e1,c1]]*u[b1,TRIANG[e1,c1]]) for c1 in 1:dom.DIMEN+1)) + | ||
| a / (8*dom.AREA[e1]^2)*( | ||
| u[b1,TRIANG[e1,1]]^2*(EDGE[e1,2,1]^2 + EDGE[e1,2,2]^2) + | ||
| u[b1,TRIANG[e1,2]]^2*(EDGE[e1,3,1]^2 + EDGE[e1,3,2]^2) + | ||
| u[b1,TRIANG[e1,3]]^2*(EDGE[e1,1,1]^2 + EDGE[e1,1,2]^2) + | ||
| 2*u[b1,TRIANG[e1,1]]*u[b1,TRIANG[e1,2]]*(EDGE[e1,2,1]*EDGE[e1,3,1] + EDGE[e1,2,2]*EDGE[e1,3,2]) + | ||
| 2*u[b1,TRIANG[e1,1]]*u[b1,TRIANG[e1,3]]*(EDGE[e1,2,1]*EDGE[e1,1,1] + EDGE[e1,2,2]*EDGE[e1,1,2]) + | ||
| 2*u[b1,TRIANG[e1,2]]*u[b1,TRIANG[e1,3]]*(EDGE[e1,1,1]*EDGE[e1,3,1] + EDGE[e1,1,2]*EDGE[e1,3,2]) | ||
| ) | ||
| ) | ||
| end | ||
| for b1 in 1:dom.BREAK+2 | ||
| energy[b1] = sum(integral[b1, e1] for e1 in 1:dom.ELEM) | ||
| end | ||
| end | ||
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| function _initial_position!(problem::PDEProblem, d::PDEDiscretizationDomain, niter) | ||
| ubar = zeros(d.NODES) | ||
| u0 = zeros(d.BREAK+2, d.NODES) | ||
| energy0 = zeros(d.BREAK+2) | ||
| integral0 = zeros(d.BREAK+2, d.ELEM) | ||
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| # Calculate an ending point on the other side of the barrier | ||
| for i in 1:niter | ||
| for b1 in 1:d.BREAK+2, n in 1:d.NODES | ||
| u0[b1, n] = (1 - (b1-1)/(d.BREAK+1))*d.US[n] + ((b1-1)/(d.BREAK+1))*d.UE[n] | ||
| end | ||
| _update_values!(integral0, energy0, u0, problem, d) | ||
| if energy0[end] < 0 | ||
| break | ||
| end | ||
| d.UE .*= 2.0 | ||
| end | ||
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| # Backtrack to the barrier to get a better representation | ||
| ubar .= d.US | ||
| for i in 1:niter | ||
| for b1 in 1:d.BREAK+2, n in 1:d.NODES | ||
| u0[b1, n] = (1 - (b1-1)/(d.BREAK+1))*ubar[n] + ((b1-1)/(d.BREAK+1))*d.UE[n] | ||
| end | ||
| _update_values!(integral0, energy0, u0, problem, d) | ||
| ebar = maximum(energy0[b1] for b1 in 1:d.BREAK+2 if energy0[b1] < 0.0) | ||
| bbar = minimum(b1 for b1 in 1:d.BREAK+2 if energy0[b1] == ebar) | ||
| ubar .= u0[bbar-1, :] | ||
| d.UE .= u0[bbar, :] | ||
| end | ||
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| for b1 in 1:d.BREAK+2, n in 1:d.NODES | ||
| u0[b1, n] = (1 - (b1-1)/(d.BREAK+1))*d.US[n] + ((b1-1)/(d.BREAK+1))*d.UE[n] | ||
| end | ||
| _update_values!(integral0, energy0, u0, problem, d) | ||
| z0 = maximum(energy0[b1] for b1 in 1:d.BREAK+2) | ||
| return ( | ||
| u=u0, energy=energy0, integral=integral0, z=z0, | ||
| ) | ||
| end | ||
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| function _transition_state_model(problem, dom::PDEDiscretizationDomain; T = Float64, backend = nothing, kwargs...) | ||
| a, b, c, d, p = problem.a, problem.b, problem.c, problem.d, problem.p | ||
| x0 = _initial_position!(problem, dom, 10) | ||
| _proto_model() | ||
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| ALPHA = 2.0 | ||
| H = ALPHA / (dom.BREAK+1) * sqrt(sum((dom.US[n] - dom.UE[n])^2 for n in 1:dom.NODES)) | ||
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| # Build optimization problem | ||
| core = ExaModels.ExaCore(T; backend= backend) | ||
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| u = ExaModels.variable(core, 1:dom.BREAK+2, 1:dom.NODES; start=x0.u) | ||
| integral = ExaModels.variable(core, 1:dom.BREAK+2, 1:dom.ELEM) | ||
| z = ExaModels.variable(core, 1; start=x0.z) | ||
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| ExaModels.objective(core, z[1]) | ||
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| ExaModels.constraint( | ||
| core, | ||
| sum(integral[b1+1, e1] for e1 in 1:n) - z[1] | ||
| for b1 in 2:dom.ELEMS+1; | ||
| lcon=-Inf, | ||
| ucon=0.0, | ||
| ) | ||
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There was a problem hiding this comment. These constraints can benefit significantly from Consider reformulating this as c = ExaModels.constraint(
core,
- z[1] for b1 in 2:dom.ELEMS+1;
lcon=-Inf,
ucon=0.0,
)
ExaModels.constraint!(
core,
b1 -1 => integral[b1+1, e1] for b1 in 2:dom.ELEMS+1
) |
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| ExaModels.constraint( | ||
| core, | ||
| sum((u[b1+1, n] - u[b1, n])^2 for n in 1:dom.NODES) | ||
| for b1 in 1:dom.BREAK+1; | ||
| lcon=-Inf, | ||
| ucon=H^2, | ||
| ) | ||
| ExaModels.constraint( | ||
| core, | ||
| dom.AREA[e1]*( | ||
| 1 / (dom.DIMEN+1) * | ||
| (sum((b[dom.TRIANG[e1,c1]]*u[b1,dom.TRIANG[e1,c1]]^2/2- | ||
| c[dom.TRIANG[e1,c1]]*u[b1,dom.TRIANG[e1,c1]]^(p[dom.TRIANG[e1,c1]]+1)/(p[dom.TRIANG[e1,c1]]+1)+ | ||
| d[dom.TRIANG[e1,c1]]*u[b1,dom.TRIANG[e1,c1]]) for c1 in 1:dom.DIMEN+1)) + | ||
| a / (8*dom.AREA[e1]^2)*( | ||
| u[b1,dom.TRIANG[e1,1]]^2*(dom.EDGE[e1,2,1]^2 + dom.EDGE[e1,2,2]^2) + | ||
| u[b1,dom.TRIANG[e1,2]]^2*(dom.EDGE[e1,3,1]^2 + dom.EDGE[e1,3,2]^2) + | ||
| u[b1,dom.TRIANG[e1,3]]^2*(dom.EDGE[e1,1,1]^2 + dom.EDGE[e1,1,2]^2) + | ||
| 2*u[b1,dom.TRIANG[e1,1]]*u[b1,dom.TRIANG[e1,2]]*(dom.EDGE[e1,2,1]*dom.EDGE[e1,3,1] + dom.EDGE[e1,2,2]*dom.EDGE[e1,3,2]) + | ||
| 2*u[b1,dom.TRIANG[e1,1]]*u[b1,dom.TRIANG[e1,3]]*(dom.EDGE[e1,2,1]*dom.EDGE[e1,1,1] + dom.EDGE[e1,2,2]*dom.EDGE[e1,1,2]) + | ||
| 2*u[b1,dom.TRIANG[e1,2]]*u[b1,dom.TRIANG[e1,3]]*(dom.EDGE[e1,1,1]*dom.EDGE[e1,3,1] + dom.EDGE[e1,1,2]*dom.EDGE[e1,3,2]) | ||
| ) | ||
| ) - integral[b1, e1] | ||
| for b1 in 1:dom.BREAK+2, e1 in 1:dom.ELEM | ||
| ) | ||
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| # Boundary | ||
| boundary_nodes = findall(isequal(1), dom.BNDRY) | ||
| ExaModels.constraint( | ||
| core, | ||
| u[b1+1, n] for b1 in 1:dom.BREAK, n in boundary_nodes | ||
| ) | ||
| ExaModels.constraint( | ||
| core, | ||
| u[1, n] for n in 1:dom.NODES; | ||
| lcon=dom.US, | ||
| ucon=dom.US, | ||
| ) | ||
| ExaModels.constraint( | ||
| core, | ||
| u[dom.BREAK+2, n] for n in 1:dom.NODES | ||
| lcon=dom.UE, | ||
| ucon=dom.UE, | ||
| ) | ||
| return core | ||
| end | ||
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| function dirichlet_model(nh) | ||
| dom = PDEDiscretizationDomain(nh, CIRCLE_DOMAIN) | ||
| println(dom.ELEM) | ||
| pb = PDEProblem( | ||
| 0.01, | ||
| fill(1.0, dom.NODES), | ||
| fill(1.0, dom.NODES), | ||
| fill(0.0, dom.NODES), | ||
| fill(3.0, dom.NODES), | ||
| ) | ||
| return _transition_state_model(pb, dom) | ||
| end | ||
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| function henon_model(nh) | ||
| dom = PDEDiscretizationDomain(nh, CIRCLE_REC_DOMAIN) | ||
| pb = PDEProblem( | ||
| 1.0, | ||
| fill(0.0, dom.NODES), | ||
| sqrt.(dom.COORDS[:, 1].^2 .+ dom.COORDS[:, 2].^2), | ||
| fill(0.0, dom.NODES), | ||
| fill(3.0, dom.NODES), | ||
| ) | ||
| return _transition_state_model(pb, dom) | ||
| end | ||
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| function lane_emden_model(nh) | ||
| dom = PDEDiscretizationDomain(nh, RECTANGLE_DOMAIN) | ||
| pb = PDEProblem( | ||
| 1.0, | ||
| fill(0.0, dom.NODES), | ||
| fill(1.0, dom.NODES), | ||
| fill(0.0, dom.NODES), | ||
| fill(3.0, dom.NODES), | ||
| ) | ||
| return _transition_state_model(pb, dom) | ||
| end | ||
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these files are not committed