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Merge pull request #1033 from utkarsh530/FRK65
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Zero Dissipation ERK6(5)
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@ChrisRackauckas
ChrisRackauckas committed Feb 22, 2020
2 parents 46b4763 + c15a279 commit 75ec5dd
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Showing 6 changed files with 376 additions and 2 deletions.
2 changes: 1 addition & 1 deletion src/OrdinaryDiffEq.jl
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Expand Up @@ -176,7 +176,7 @@ module OrdinaryDiffEq

export FunctionMap, Euler, Heun, Ralston, Midpoint, RK4, ExplicitRK, OwrenZen3, OwrenZen4, OwrenZen5,
BS3, BS5, RK46NL, DP5, Tsit5, DP8, Vern6, Vern7, Vern8, TanYam7, TsitPap8,
Vern9, Feagin10, Feagin12, Feagin14, CompositeAlgorithm, Anas5, RKO65
Vern9, Feagin10, Feagin12, Feagin14, CompositeAlgorithm, Anas5, RKO65, FRK65

export SSPRK22, SSPRK33, SSPRK53, SSPRK53_2N1, SSPRK53_2N2, SSPRK63, SSPRK73, SSPRK83, SSPRK432,
SSPRKMSVS32, SSPRKMSVS43, SSPRK932, SSPRK54, SSPRK104
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3 changes: 2 additions & 1 deletion src/alg_utils.jl
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Expand Up @@ -25,6 +25,7 @@ isfsal(alg::NDBLSRK144) = false
isfsal(alg::PDIRK44) = false
isfsal(alg::DImplicitEuler) = false
isfsal(alg::RKO65) = false
isfsal(alg::FRK65) = true

get_current_isfsal(alg, cache) = isfsal(alg)
get_current_isfsal(alg::CompositeAlgorithm, cache) = isfsal(alg.algs[cache.current])
Expand Down Expand Up @@ -164,7 +165,7 @@ alg_order(alg::Anas5) = 5
alg_order(alg::RK46NL) = 4
alg_order(alg::KuttaPRK2p5) = 5
alg_order(alg::RKO65) = 5

alg_order(alg::FRK65) = 6

alg_order(alg::SymplecticEuler) = 1
alg_order(alg::VelocityVerlet) = 2
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5 changes: 5 additions & 0 deletions src/algorithms.jl
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Expand Up @@ -398,6 +398,11 @@ struct Vern9 <: OrdinaryDiffEqAdaptiveAlgorithm
lazy::Bool
Vern9(;lazy=true) = new(lazy)
end
struct FRK65{T} <: OrdinaryDiffEqAdaptiveAlgorithm
omega::T
FRK65(omega=0.0) = new{typeof(omega)}(omega)
end


################################################################################

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245 changes: 245 additions & 0 deletions src/caches/low_order_rk_caches.jl
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Expand Up @@ -617,3 +617,248 @@ function alg_cache(alg::RKO65,u,rate_prototype,uEltypeNoUnits,uBottomEltypeNoUni
tab = RKO65ConstantCache(constvalue(uBottomEltypeNoUnits),constvalue(tTypeNoUnits))
RKO65Cache(u,uprev,k, k1,k2,k3,k4,k5,k6, tmp, fsalfirst, tab)
end

@cache struct FRK65Cache{uType,rateType,uNoUnitsType,TabType} <: OrdinaryDiffEqMutableCache
u::uType
uprev::uType
utilde::uType
k1::rateType
k2::rateType
k3::rateType
k4::rateType
k5::rateType
k6::rateType
k7::rateType
k8::rateType
k9::rateType
tmp::uType
atmp::uNoUnitsType
tab::TabType
end

struct FRK65ConstantCache{T1,T2} <: OrdinaryDiffEqConstantCache

α21::T1
α31::T1
α41::T1
α51::T1
α61::T1
α71::T1
α81::T1
α91::T1

α32::T1

α43::T1
α53::T1
α63::T1
α73::T1
α83::T1

α54::T1
α64::T1
α74::T1
α84::T1
α94::T1

α65::T1
α75::T1
α85::T1
α95::T1

α76::T1
α86::T1
α96::T1

α87::T1
α97::T1

α98::T1

β1::T1
# β4::T1
# β5::T1
# β6::T1
β7::T1
β8::T1

β1tilde::T1
β4tilde::T1
β5tilde::T1
β6tilde::T1
β7tilde::T1
β8tilde::T1
β9tilde::T1

c2::T2
c3::T2
c4::T2
c5::T2
c6::T2
c7::T2
c8::T2
c9::T2

d1::T1
d2::T1
d3::T1
d4::T1
d5::T1
d6::T1
d7::T1
d8::T1
d9::T1
d10::T1
d11::T1
d12::T1
d13::T1

e1::T1
e2::T1
e3::T1
e4::T1
e5::T1
e6::T1
e7::T1
e8::T1
e9::T1
e10::T1
e11::T1

f1::T1
f2::T1
f3::T1
f4::T1
f5::T1
f6::T1
f7::T1
f8::T1
f9::T1
f10::T1
f11::T1

function FRK65ConstantCache(T1,T2)

# elements of Butcher Table
α21 = T1(1//89)
α31 = T1(-38624//142129)
α41 = T1(51//1508)
α51 = T1(3259284578//3517556363)
α61 = T1(-108363632681//45875676369)
α71 = T1(7137368591//11299833148)
α81 = T1(8898824396//9828950919)
α91 = T1(1026331676//33222204855)

α32 = T1(51442//142129)

α43 = T1(153//1508)
α53 = T1(-69727055112//19553806387)
α63 = T1(80902506271//8700424616)
α73 = T1(-33088067061//10572251159)
α83 = T1(25673454973//11497947835)


α54 = T1(36230363390//11788838981)
α64 = T1(-120088218786//17139312481)
α74 = T1(11481363823//3650030081)
α84 = T1(-74239028301//15737704666)
α94 = T1(1450675392//5936579813)

α65 = T1(4533285649//6676940598)
α75 = T1(-4096673444//7349814937)
α85 = T1(222688842816//44196813415)
α95 = T1(4617877550//16762182457)

α76 = T1(9911918171//12847192605)
α86 = T1(-105204445705//30575217706)
α96 = T1(1144867463//6520294355)

α87 = T1(8799291910//8966990271)
α97 = T1(1822809703//7599996644)

α98 = T1(79524953//2351253316)

β1 = T1(1026331676//33222204855)
#β4 = T1(1450675392//5936579813)
#β5 = T1(4617877550//16762182457)
#β6 = T1(1144867463//6520294355)
β7 = T1(1822809703//7599996644)
β8 = T1(79524953//2351253316)

β1tilde = T1(413034411//13925408836)
β4tilde = T1(1865954212//7538591735)
β5tilde = T1(4451980162//16576017119)
β6tilde = T1(1157843020//6320223511)
β7tilde = T1(802708729//3404369569)
β8tilde = T1(-251398161//17050111121)
β9tilde = T1(1//20)

c2 = T2(1//89)
c3 = T2(34//377)
c4 = T2(51//377)
c5 = T2(14497158//33407747)
c6 = T2(9744566553//16002998914)
c7 = T2(330//383)
c8 = T2(1//1)
c9 = T2(1//1)

d1 = T1(140209127//573775965)
d2 = T1(-8530039//263747097)
d3 = T1(-308551//104235790)
d4 = T1(233511//333733259)
d5 = T1(9126//184950985)
d6 = T1(22//50434083)
d7 = T1(19//424427471)
d8 = T1(-28711//583216934059)
d9 = T1(-3831531//316297807)
d10 = T1(551767//187698280)
d11 = T1(9205//210998423)
d12 = T1(-250//519462673)
d13 = T1(67//327513887)

e1=T1(437217689//1587032700)
e2=T1(-15824413//592362279)
e3=T1(-1563775//341846569)
e4=T1(270497//369611210)
e5=T1(-26623//453099487)
e6=T1(-616297487849)
e7=T1(-47682337//491732789)
e8=T1(-4778275//287766311)
e9=T1(641177//265376522)
e10=T1(44633//291742143)
e11=T1(611//223639880)

f1=T1(44861261//255495624)
f2=T1(-11270940//352635157)
f3=T1(-182222//232874507)
f4=T1(164263//307215200)
f5=T1(32184//652060417)
f6=T1(-352//171021903)
f7=T1(-18395427//101056291)
f8=T1(-621686//139501937)
f9=T1(2030024//612171255)
f10=T1(-711049//7105160932)
f11=T1(267//333462710)

new{T1,T2}(α21, α31, α41, α51, α61, α71, α81, α91, α32, α43, α53, α63, α73, α83, α54, α64, α74, α84, α94, α65, α75, α85, α95, α76, α86, α96, α87, α97, α98, β1, β7, β8, β1tilde, β4tilde, β5tilde, β6tilde, β7tilde, β8tilde, β9tilde, c2, c3, c4, c5, c6, c7, c8, c9, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, d11, d12, d13, e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11)
end
end

alg_cache(alg::FRK65,u,rate_prototype,uEltypeNoUnits,uBottomEltypeNoUnits,tTypeNoUnits,uprev,uprev2,f,t,dt,reltol,p,calck,::Val{false}) = FRK65ConstantCache(constvalue(uBottomEltypeNoUnits),constvalue(tTypeNoUnits))

function alg_cache(alg::FRK65,u,rate_prototype,uEltypeNoUnits,uBottomEltypeNoUnits,tTypeNoUnits,uprev,uprev2,f,t,dt,reltol,p,calck,::Val{true})
tab = FRK65ConstantCache(constvalue(uBottomEltypeNoUnits),constvalue(tTypeNoUnits))
k1 = zero(rate_prototype)
k2 = zero(rate_prototype)
k3 = zero(rate_prototype)
k4 = zero(rate_prototype)
k5 = zero(rate_prototype)
k6 = zero(rate_prototype)
k7 = zero(rate_prototype)
k8 = zero(rate_prototype)
k9 = zero(rate_prototype)
utilde = similar(u)
atmp = similar(u,uEltypeNoUnits)
tmp = similar(u)
FRK65Cache(u, uprev, utilde, k1, k2, k3, k4, k5, k6, k7, k8, k9, tmp, atmp, tab)
end
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