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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Languages: English
Types: Doctoral thesis
Subjects: QE
The thesis concludes with the development of a numerical model for a real case study in the United Kingdom, which is one of the first examples of formal characterization of model uncertainty for an actual site.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • M ix e d a n d H y b r id F i n i t e E le m e n t T h e o r y 2.1 I n t r o d u c t i o n ................................................................................................
    • 2.2 T h e m athem atical m o d e l ..........................................................................
    • 2.3 Prelim inary D e fin itio n s .............................................................................
    • 2.4 C ontinuous Weak F o r m .............................................................................
    • 2.5 Mixed F in ite Element A p p ro x im a tio n ..................................................... 2.5.1 R aviart-Thom as A p p ro x im a tio n .................................................. 2.5.2 Linear S y s t e m ................................................................................. 2.5.3 Solution S t r a t e g i e s ........................................................................
    • 2.6 Mixed Hybrid Finite Element M e th o d ..................................................... 2.6.1 Solution S t r a t e g i e s ........................................................................
    • M ix e d a n d H y b r id F in ite E le m e n t N u m e r ic a l E x p e r im e n ts 3.1 I n t r o d u c t i o n ................................................................................................
    • 3.2 Numerical experiments on triangular m e s h e s ........................................ 3.2.1 Problem 1: heterogeneous, isotropic and diagonal C ................ 3.2.2 Problem 2: heterogeneous, anisotropic and diagonal C ............ 3.2.3 Problem 3: heterogeneous, anisotropic and full-tensor C . . . 3.2.4 Problem 4: discontinuous, anisotropic and full-tensor C . . . 3.2.5 Problem 5: distorted triangular m e s h .........................................
    • 3.3 Numerical experiments on rectangular m e s h e s ..................................... 3.3.1 Problem 1: heterogeneous, isotropic and diagonal C ................ 3.3.2 Problem 2: heterogeneous, anisotropic and diagonal C ............ 3.3.3 Problem 3: heterogeneous, anisotropic and full-tensor C . . . 3.3.4 Problem 4: discontinuous, anisotropic and full-tensor C . . .
    • 3.3.5 Problem 5: distorted rectangular m e s h ......................................
    • S p e c tr a l S t o c h a s tic F in it e E le m e n t T h e o r y 4.1 I n t r o d u c t i o n .................................................................................................
    • 4.2 T he m athem atical m o d e l ...........................................................................
    • 4.3 Hydraulic Conductivity Coefficient A p p ro x im a tio n ................................
    • 4.4 T h e weak formulation .............................................................................. 4.4.1 Prim al F o r m u la tio n ........................................................................ 4.4.2 Mixed F o r m u l a t i o n ........................................................................
    • 4.5 Stochastic Finite Element A p p ro x im a tio n ............................................... 4.5.1 Polynomial C h a o s ........................................................................... 4.5.2 Linear S y s t e m .................................................................................. 4.5.3 Im plem entation and Solution S tr a te g ie s ......................................
    • 4.6 Stochastic Mixed Finite Element A p p ro x im a tio n ................................... 4.6.1 Linear S y s t e m .................................................................................. 4.6.2 Im plem entation and Solution S tr a te g ie s ......................................
    • 4.7 Stochastic Mixed Hybrid F o r m u la tio n ..................................................... 4.7.1 Im plem entation and Solution S tr a te g ie s ......................................
    • C o m p a r iso n o f S t o c h a s t ic G a le r k in a n d M o n te C arlo M e t h o d s I n t r o d u c t i o n ............................................................................................... SFEM vs Monte Carlo S i m u l a t i o n s ........................................................ 5.2.1 Test Problem 1 - Hermite p o l y n o m i a l s ..................................... 5.2.2 Test Problem 2 - Legendre p o ly n o m ia ls ..................................... SMFEM vs Monte Carlo S i m u l a t i o n s ...................................................... 5.3.1 Test Problem 1 - Hermite p o l y n o m i a l s ..................................... 5.3.2 Test Problem 2 - variable a ....................................................... C o n c l u s i o n s ...............................................................................................
    • S o lu tio n S t r a t e g ie s for S to c h a stic G a lerk in t i c C a se 6.1 I n t r o d u c t i o n ...............................................................................................
    • 6.2 SFEM s o l v e r s .............................................................................................. 6.2.1 Block-diagonal p r e c o n d it io n e r ...................................................... 6.2.2 Block Symmetric Gauss-Seidel P r e c o n d i t i o n e r ......................... 6.2.3 Gauss Seidel S o l v e r s ......................................................................
    • 6.3 Comparison and C onclusions...................................................................
    • 6.4 SMFEM s o l v e r s ........................................................................................... 6.4.1 Schur complement p r e c o n d it io n e r ............................................... 6.4.2 C o n c l u s i o n s .....................................................................................
    • 7.3.1 SFEM vs Monte Carlo S i m u l a t i o n s ............................................
    • 7.3.2 SMFEM vs Monte Carlo S i m u l a t i o n s .........................................
    • 7.4.1 Block-diagonal p r e c o n d i t i o n e r .....................................................
    • 7.4.2 Block Symmetric Gauss-Seidel P r e c o n d i t i o n e r ..........................
    • 7.4.3 Gauss Seidel S o l v e r s .....................................................................
    • 7.6.1 Schur complement p r e c o n d i t i o n e r ...............................................
    • 7.6.2 C o n c l u s io n s .....................................................................................
    • 3.3 MFEM solutions and source term for a = 1 - Test problem 3 .............
    • 3.4 MFEM solutions for a = 1 ,102 - Test problem 4 ...................................
    • 3.5 Structured and perturbed triangular finite element mesh for h = ^ - Test problem 5 ..........................................................................................
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