SLEPc: Scalable Library for Eigenvalue Problem Computations Jose ...

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SLEPc Criticality Criticality: depends on how many of the free neutrons from each fission, on average, hits another U-235 nucleus and causes it to split: • Exactly one: the mass is critical – The mass will exist at a stable temperature • Less than one: the mass is subcritical – Eventually, induced fission will end in the mass • More than one: the mass is supercritical – It will heat up – In a nuclear reactor, the reactor core needs to be slightly supercritical so that plant operators can raise and lower the temperature of the reactor – The control rods give the operators a way to absorb free neutrons so that the reactor can be maintained at a critical level
SLEPc The Physical Problem • Lambda Modes equation – Derived from time-independent neutron diffusion equation – Multigroup approach: neutrons are grouped in energy intervals. With two energy groups (fast and thermal): L = ⎡− ∇ ⎢ ⎣ M = ( D ∇) + Σ 1 ⎡v ⎢ ⎣ 1 − Σ Σ 0 f 1 Lφ = 12 i a1 v 2 + Σ Σ 0 1 Mφi λ f i 2 12 ⎤ ⎥ ⎦ − ∇( D φ = i 2 0 ∇) ⎡φ fi ⎢ ⎣φti + Σ ⎤ ⎥ ⎦ a2 ⎤ ⎥ ⎦
Page 1 and 2: SLEPc SLEPc ACTS Workshop - LBNL, O
Page 3 and 4: SLEPc Acceleration • Convergence
Page 5 and 6: SLEPc SLEPc Objectives • Current
Page 7 and 8: SLEPc Numerical Components Nonlinea
Page 9 and 10: SLEPc SLEPc SLEPc objects (2) ST: S
Page 11 and 12: SLEPc Power Method • power - Powe
Page 13 and 14: SLEPc Arnoldi, Lanczos and Wrappers
Page 15 and 16: SLEPc The Future • First version:
Page 17: SLEPc Introduction • Context: Sec
Page 21 and 22: SLEPc Nodalization 2D Case All axia
Page 23 and 24: SLEPc Analysis of Results • Physi
Page 25 and 26: SLEPc Solution Strategy • Large e
Page 27 and 28: SLEPc Matrix Generation typedef str
Page 29: SLEPc Preliminary Performance Resul

SLEPc: Scalable Library for Eigenvalue Problem Computations Jose ...

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