Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential ...Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.展开更多
We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares func...We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw^2- and Hw^-1- norm of the residual equations and then we eplace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.展开更多
To the Editor:A 63-year-old male patient was referred from a local clinic for diffuse abdominal pain for 1 day and ruptured abdominal aortic aneurysm (rAAA) in computed tomography (CT).He denied any medical history of...To the Editor:A 63-year-old male patient was referred from a local clinic for diffuse abdominal pain for 1 day and ruptured abdominal aortic aneurysm (rAAA) in computed tomography (CT).He denied any medical history of hypertension,diabetes mellitus,hepatitis or pneumonia.The patient’s blood pressure was 100/70 mmHg with a pulse rate of 105 beats/min and a body temperature of 37.1℃.The Abdomen was mildly distended with diffuse pain and tenderness.展开更多
To the Editor:A 71-year-old male patient was referred for incidentally delayed type Ib_endoleak_on computed tomographic angiography(CTA).He had been performed endovascular abdominal aortic aneurysm repair(EVAR)with th...To the Editor:A 71-year-old male patient was referred for incidentally delayed type Ib_endoleak_on computed tomographic angiography(CTA).He had been performed endovascular abdominal aortic aneurysm repair(EVAR)with the Zenith(Cook Inc,Bloomington,IN,USA)stent-grafts for right common iliac artery(CIA)aneurysm with a diameter of 4.4 cm at 17 months ago.展开更多
This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed least-squares functional is defined as the sum of ...This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed least-squares functional is defined as the sum of the L2- and H-1-norms of the residual equations weighted appropriately. The minus one norm in the functional is replaced by the discrete minus one norm and then the discrete minus one norm least-squares methods are analyzed with various numerical results focusing on the finite element accuracy and multigrid convergence performances.展开更多
This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations.As with our earlier work on a velocity control by the Stokes flow in[S.Ryu,H.-C.L...This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations.As with our earlier work on a velocity control by the Stokes flow in[S.Ryu,H.-C.Lee and S.D.Kim,SIAM J.Numer.Anal.,47(2009),pp.1524-1545],we recast the objective functional as a H1 seminorm in the velocity control term.By introducing a velocity-flux variable and using the Lagrange multiplier rule,a first-order optimality system is obtained.We show that the least-squares principle based on L2 norms applied to this system yields the optimal discretization error estimates for each variable in H1 norm,including the velocity flux.For numerical tests,multigrid method is employed to the discrete algebraic system,so that the velocity and flux controls are obtained.展开更多
The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to Lu := - u' with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The con...The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to Lu := - u' with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The condition number of the resulting system behaves like O(1/h) where h is the mesh size. We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to O(1).展开更多
To the Editor： An 84-year-old male was referred from a local clinic for an incidental thoracoabdominal aortic aneurysm （TAAA） presenting in a supraceliac aortic aneurysm （SCAA） with maximal diameter of 6.0 cm in ...To the Editor： An 84-year-old male was referred from a local clinic for an incidental thoracoabdominal aortic aneurysm （TAAA） presenting in a supraceliac aortic aneurysm （SCAA） with maximal diameter of 6.0 cm in spine magnetic resonance imaging. He had a medical history of hypertension and chronic obstructive pulmonary disease, and was a 30 pack-years＇ smoker. On physical exalnination, his vital signs were stable and abdomen was soft without pain and tenderness. Laboratory findings showed white blood cell count of 4840/μl, serum creatinine of 9 mg/L, erythrocyte sedimentation rate of 16 mm/h, and c-reactive protein of 13.24 mg/L.展开更多
To the Editor： A 67-year-old female was referred for persisted swelling in right leg despite of anticoagulation during 2 months for deep vein thrombosis （DVT） of the right popliteal vein （PV）. Initial duplex ultr...To the Editor： A 67-year-old female was referred for persisted swelling in right leg despite of anticoagulation during 2 months for deep vein thrombosis （DVT） of the right popliteal vein （PV）. Initial duplex ultrasonography of local clinic at 2 months ago showed the acute DVT of right PV with thrombus and dilated vein [Figure 1a].展开更多
文摘Finite difference type preconditioners for spectral element discretizations based on Legendre-Gauss-Lobatto points are analyzed. The latter is employed for the approximation of uniformly elliptic partial differential problems. In this work, it is shown that the condition number of the resulting preconditioned system is bounded independently of both of the polynomial degrees used in the spectral element method and the element sizes. Several numerical tests verify the h-p independence of the proposed preconditioning.
文摘We develop and analyze a first-order system least-squares spectral method for the second-order elhptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lw^2- and Hw^-1- norm of the residual equations and then we eplace the negative norm by the discrete negative norm and analyze the discrete Chebyshev weighted least-squares method. The spectral convergence is derived for the proposed method. We also present various numerical experiments. The Legendre weighted least-squares method can be easily developed by following this paper.
文摘To the Editor:A 63-year-old male patient was referred from a local clinic for diffuse abdominal pain for 1 day and ruptured abdominal aortic aneurysm (rAAA) in computed tomography (CT).He denied any medical history of hypertension,diabetes mellitus,hepatitis or pneumonia.The patient’s blood pressure was 100/70 mmHg with a pulse rate of 105 beats/min and a body temperature of 37.1℃.The Abdomen was mildly distended with diffuse pain and tenderness.
文摘To the Editor:A 71-year-old male patient was referred for incidentally delayed type Ib_endoleak_on computed tomographic angiography(CTA).He had been performed endovascular abdominal aortic aneurysm repair(EVAR)with the Zenith(Cook Inc,Bloomington,IN,USA)stent-grafts for right common iliac artery(CIA)aneurysm with a diameter of 4.4 cm at 17 months ago.
基金The paper was supported by Korea Research Foundation Grant (KRF-2002-070-C00014).
文摘This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed least-squares functional is defined as the sum of the L2- and H-1-norms of the residual equations weighted appropriately. The minus one norm in the functional is replaced by the discrete minus one norm and then the discrete minus one norm least-squares methods are analyzed with various numerical results focusing on the finite element accuracy and multigrid convergence performances.
基金This work was supported by Korea Research Foundation under grant KRF-2005-070-C00017.
文摘This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations.As with our earlier work on a velocity control by the Stokes flow in[S.Ryu,H.-C.Lee and S.D.Kim,SIAM J.Numer.Anal.,47(2009),pp.1524-1545],we recast the objective functional as a H1 seminorm in the velocity control term.By introducing a velocity-flux variable and using the Lagrange multiplier rule,a first-order optimality system is obtained.We show that the least-squares principle based on L2 norms applied to this system yields the optimal discretization error estimates for each variable in H1 norm,including the velocity flux.For numerical tests,multigrid method is employed to the discrete algebraic system,so that the velocity and flux controls are obtained.
基金The paper was supported by KOSEF 1999-1-103-002-3.
文摘The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to Lu := - u' with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The condition number of the resulting system behaves like O(1/h) where h is the mesh size. We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to O(1).
文摘To the Editor： An 84-year-old male was referred from a local clinic for an incidental thoracoabdominal aortic aneurysm （TAAA） presenting in a supraceliac aortic aneurysm （SCAA） with maximal diameter of 6.0 cm in spine magnetic resonance imaging. He had a medical history of hypertension and chronic obstructive pulmonary disease, and was a 30 pack-years＇ smoker. On physical exalnination, his vital signs were stable and abdomen was soft without pain and tenderness. Laboratory findings showed white blood cell count of 4840/μl, serum creatinine of 9 mg/L, erythrocyte sedimentation rate of 16 mm/h, and c-reactive protein of 13.24 mg/L.
文摘To the Editor： A 67-year-old female was referred for persisted swelling in right leg despite of anticoagulation during 2 months for deep vein thrombosis （DVT） of the right popliteal vein （PV）. Initial duplex ultrasonography of local clinic at 2 months ago showed the acute DVT of right PV with thrombus and dilated vein [Figure 1a].
