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Integrators.H
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1/* Copyright 2022-2023 The Regents of the University of California, through Lawrence
2 * Berkeley National Laboratory (subject to receipt of any required
3 * approvals from the U.S. Dept. of Energy). All rights reserved.
4 *
5 * This file is part of ImpactX.
6 *
7 * Authors: Chad Mitchell, Axel Huebl
8 * License: BSD-3-Clause-LBNL
9 */
10#ifndef IMPACTX_INTEGRATORS_H_
11#define IMPACTX_INTEGRATORS_H_
12
13#include <AMReX_Extension.H> // for AMREX_RESTRICT
14#include <AMReX_REAL.H> // for ParticleReal
15
16
17namespace impactx::integrators
18{
19
34 template <typename T_Element>
35 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
36 void symp2_integrate (
37 RefPart & refpart,
38 amrex::ParticleReal const zin,
39 amrex::ParticleReal const zout,
40 int const nsteps,
41 T_Element const & element
42 )
43 {
44 using namespace amrex::literals; // for _rt and _prt
45
46 // initialize numerical integration parameters
47 amrex::ParticleReal const dz = (zout-zin)/nsteps;
48 amrex::ParticleReal const tau1 = dz*0.5_prt;
49 amrex::ParticleReal const tau2 = dz;
50
51 // initialize the value of the independent variable
52 amrex::ParticleReal zeval = zin;
53
54 // loop over integration steps
55 for(int j=0; j < nsteps; ++j)
56 {
57 element.map1(tau1,refpart,zeval);
58 element.map2(tau2,refpart,zeval);
59 element.map1(tau1,refpart,zeval);
60 }
61 }
62
77 template <typename T_Element>
78 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
79 void symp2_integrate_split3 (
80 RefPart & refpart,
81 amrex::ParticleReal const zin,
82 amrex::ParticleReal const zout,
83 int const nsteps,
84 T_Element const & element
85 )
86 {
87 using namespace amrex::literals; // for _rt and _prt
88
89 // initialize numerical integration parameters
90 amrex::ParticleReal const dz = (zout-zin)/nsteps;
91 amrex::ParticleReal const tau1 = dz*0.5_prt;
92 amrex::ParticleReal const tau2 = dz*0.5_prt;
93 amrex::ParticleReal const tau3 = dz;
94
95 // initialize the value of the independent variable
96 amrex::ParticleReal zeval = zin;
97
98 // loop over integration steps
99 for(int j=0; j < nsteps; ++j)
100 {
101 element.map1(tau1,refpart,zeval);
102 element.map2(tau2,refpart,zeval);
103 element.map3(tau3,refpart,zeval);
104 element.map2(tau2,refpart,zeval);
105 element.map1(tau1,refpart,zeval);
106 }
107 }
108
126 template <typename T_Element>
127 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
128 void symp4_integrate (
129 RefPart & refpart,
130 amrex::ParticleReal const zin,
131 amrex::ParticleReal const zout,
132 int const nsteps,
133 T_Element const & element
134 )
135 {
136 using namespace amrex::literals; // for _rt and _prt
137
138 // initialize numerical integration parameters
139 amrex::ParticleReal const dz = (zout-zin)/nsteps;
140 amrex::ParticleReal const alpha = 1_prt - std::pow(2_prt,1_prt/3_prt);
141 amrex::ParticleReal const tau2 = dz/(1_prt + alpha);
142 amrex::ParticleReal const tau1 = tau2*0.5_prt;
143 amrex::ParticleReal const tau3 = alpha*tau1;
144 amrex::ParticleReal const tau4 = (alpha - 1_prt)*tau2;
145
146 // initialize the value of the independent variable
147 amrex::ParticleReal zeval = zin;
148
149 // loop over integration steps
150 for (int j=0; j < nsteps; ++j)
151 {
152 element.map1(tau1,refpart,zeval);
153 element.map2(tau2,refpart,zeval);
154 element.map1(tau3,refpart,zeval);
155 element.map2(tau4,refpart,zeval);
156 element.map1(tau3,refpart,zeval);
157 element.map2(tau2,refpart,zeval);
158 element.map1(tau1,refpart,zeval);
159 }
160 }
161
176 template <typename T_Real, typename T_Element>
177 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
178 void symp2_integrate_particle (
179 amrex::SmallVector<T_Real, 6, 1> & particle,
180 amrex::ParticleReal const zin,
181 amrex::ParticleReal const zout,
182 int const nsteps,
183 T_Element const & element
184 )
185 {
186 using namespace amrex::literals; // for _rt and _prt
187
188 // initialize numerical integration parameters
189 amrex::ParticleReal const dz = (zout-zin)/nsteps;
190 amrex::ParticleReal const tau1 = dz*0.5_prt;
191 amrex::ParticleReal const tau2 = dz;
192
193 // initialize the value of the independent variable
194 amrex::ParticleReal zeval = zin;
195
196 // loop over integration steps
197 for(int j=0; j < nsteps; ++j)
198 {
199 element.map1(tau1,particle,zeval);
200 element.map2(tau2,particle,zeval);
201 element.map1(tau1,particle,zeval);
202 }
203 }
204
205
223 template <typename T_Real, typename T_Element>
224 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
225 void symp4_integrate_particle (
226 amrex::SmallVector<T_Real, 6, 1> & particle,
227 amrex::ParticleReal const zin,
228 amrex::ParticleReal const zout,
229 int const nsteps,
230 T_Element const & element
231 )
232 {
233 using namespace amrex::literals; // for _rt and _prt
234
235 // initialize numerical integration parameters
236 amrex::ParticleReal const dz = (zout-zin)/nsteps;
237 amrex::ParticleReal const alpha = 1_prt - std::pow(2_prt,1_prt/3_prt);
238 amrex::ParticleReal const tau2 = dz/(1_prt + alpha);
239 amrex::ParticleReal const tau1 = tau2*0.5_prt;
240 amrex::ParticleReal const tau3 = alpha*tau1;
241 amrex::ParticleReal const tau4 = (alpha - 1_prt)*tau2;
242
243 // initialize the value of the independent variable
244 amrex::ParticleReal zeval = zin;
245
246 // loop over integration steps
247 for (int j=0; j < nsteps; ++j)
248 {
249 element.map1(tau1,particle,zeval);
250 element.map2(tau2,particle,zeval);
251 element.map1(tau3,particle,zeval);
252 element.map2(tau4,particle,zeval);
253 element.map1(tau3,particle,zeval);
254 element.map2(tau2,particle,zeval);
255 element.map1(tau1,particle,zeval);
256 }
257 }
258
259
282 template <typename T_Real, typename T_Element>
283 AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE
284 void symp6_integrate_particle (
285 amrex::SmallVector<T_Real, 6, 1> & particle,
286 amrex::ParticleReal const zin,
287 amrex::ParticleReal const zout,
288 int const nsteps,
289 T_Element const & element
290 )
291 {
292 using namespace amrex::literals; // for _rt and _prt
293
294 // initialize numerical integration parameters
295 amrex::ParticleReal const dz = (zout-zin)/nsteps;
296 amrex::ParticleReal const w0 = 1.31518632068391121888424973;
297 amrex::ParticleReal const w1 = -1.17767998417887100694641568;
298 amrex::ParticleReal const w2 = 0.23557321335935813368479318;
299 amrex::ParticleReal const w3 = 0.78451361047755726381949763;
300
301 amrex::ParticleReal const tau1 = w3 * dz / 2_prt;
302 amrex::ParticleReal const tau2 = w3 * dz;
303 amrex::ParticleReal const tau3 = (w3 + w2) * dz / 2_prt;
304 amrex::ParticleReal const tau4 = w2 * dz;
305 amrex::ParticleReal const tau5 = (w2 + w1) * dz / 2_prt;
306 amrex::ParticleReal const tau6 = w1 * dz;
307 amrex::ParticleReal const tau7 = (w1 + w0) * dz / 2_prt;
308 amrex::ParticleReal const tau8 = w0 * dz;
309
310 // initialize the value of the independent variable
311 amrex::ParticleReal zeval = zin;
312
313 // loop over integration steps
314 for (int j=0; j < nsteps; ++j)
315 {
316 element.map1(tau1,particle,zeval);
317 element.map2(tau2,particle,zeval);
318 element.map1(tau3,particle,zeval);
319 element.map2(tau4,particle,zeval);
320 element.map1(tau5,particle,zeval);
321 element.map2(tau6,particle,zeval);
322 element.map1(tau7,particle,zeval);
323 element.map2(tau8,particle,zeval);
324 element.map1(tau7,particle,zeval);
325 element.map2(tau6,particle,zeval);
326 element.map1(tau5,particle,zeval);
327 element.map2(tau4,particle,zeval);
328 element.map1(tau3,particle,zeval);
329 element.map2(tau2,particle,zeval);
330 element.map1(tau1,particle,zeval);
331 }
332 }
333
334
335} // namespace impactx::integrators
336
337#endif // IMPACTX_INTEGRATORS_H_
AMReX_Extension.H
AMREX_FORCE_INLINE
#define AMREX_FORCE_INLINE
AMREX_GPU_HOST_DEVICE
#define AMREX_GPU_HOST_DEVICE
AMReX_REAL.H
amrex::SmallVector
SmallMatrix< T, N, 1, Order::F, StartIndex > SmallVector
impactx::integrators
Definition Integrators.H:18
impactx::integrators::symp4_integrate
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp4_integrate(RefPart &refpart, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
Definition Integrators.H:128
impactx::integrators::symp4_integrate_particle
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp4_integrate_particle(amrex::SmallVector< T_Real, 6, 1 > &particle, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
Definition Integrators.H:225
impactx::integrators::symp2_integrate
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp2_integrate(RefPart &refpart, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
Definition Integrators.H:36
impactx::integrators::symp2_integrate_split3
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp2_integrate_split3(RefPart &refpart, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
Definition Integrators.H:79
impactx::integrators::symp6_integrate_particle
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp6_integrate_particle(amrex::SmallVector< T_Real, 6, 1 > &particle, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
Definition Integrators.H:284
impactx::integrators::symp2_integrate_particle
AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE void symp2_integrate_particle(amrex::SmallVector< T_Real, 6, 1 > &particle, amrex::ParticleReal const zin, amrex::ParticleReal const zout, int const nsteps, T_Element const &element)
Definition Integrators.H:178
impactx::RefPart
Definition ReferenceParticle.H:31
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